# Publications 2021

## Bath-Induced Zeno Localization in Driven Many-Body Quantum Systems – Archive ouverte HAL

### Thibaud Maimbourg

^{1}Denis M. Basko^{2}Markus Holzmann^{2}Alberto Rosso^{1}#### Thibaud Maimbourg, Denis M. Basko, Markus Holzmann, Alberto Rosso. Bath-Induced Zeno Localization in Driven Many-Body Quantum Systems.

*Phys.Rev.Lett.*, 2021, 126 (12), pp.120603. ⟨10.1103/PhysRevLett.126.120603⟩. ⟨hal-03186174⟩We study a quantum interacting spin system subject to an external drive and coupled to a thermal bath of vibrational modes, uncorrelated for different spins, serving as a model for dynamic nuclear polarization protocols. We show that even when the many-body eigenstates of the system are ergodic, a sufficiently strong coupling to the bath may effectively localize the spins due to many-body quantum Zeno effect. Our results provide an explanation of the breakdown of the thermal mixing regime experimentally observed above 4–5 K in these protocols.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPM2C - Laboratoire de physique et modélisation des milieux condensés

## Casimir-Polder shift of ground-state hyperfine Zeeman sublevels of hydrogen isotopes in a micron-sized metallic cavity at finite temperature – Archive ouverte HAL

### Davide IacobacciGiuseppe BimonteThorsten Emig

^{1}#### Davide Iacobacci, Giuseppe Bimonte, Thorsten Emig. Casimir-Polder shift of ground-state hyperfine Zeeman sublevels of hydrogen isotopes in a micron-sized metallic cavity at finite temperature.

*Phys.Rev.A*, 2021, 103 (6), pp.062811. ⟨10.1103/PhysRevA.103.062811⟩. ⟨hal-03268883⟩The frequencies of transitions between hyperfine levels of ground-state atoms can be measured with exquisite precision using magnetic-resonance techniques. This makes hyperfine transitions ideal probes of QED effects originating from the interaction of atoms with the quantized electromagnetic field. One of the most remarkable effects predicted by QED is the Casimir-Polder shift experienced by the energy levels of atoms placed near one or more dielectric objects. Here we compute the Casimir-Polder shift and the width of hyperfine transitions between ground-state Zeeman sublevels of a hydrogen atom placed in a micron-sized metallic cavity, over a range of temperatures extending from cryogenic temperatures to room temperature. Results are presented also for deuterium and tritium. We predict shifts of the hyperfine transitions frequencies of a few tens of Hz that might be measurable with present-day magnetic resonance apparatus.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Chaos-assisted long-range tunneling for quantum simulation – Archive ouverte HAL

### Maxime Martinez

^{1}Olivier Giraud^{2}Denis Ullmo^{2}Juliette Billy^{3}David Guéry-Odelin^{3}Bertrand Georgeot^{1}Gabriel Lemarié^{1, 4, 5}#### Maxime Martinez, Olivier Giraud, Denis Ullmo, Juliette Billy, David Guéry-Odelin, et al.. Chaos-assisted long-range tunneling for quantum simulation.

*Physical Review Letters*, American Physical Society, 2021, 126, pp.174102. ⟨10.1103/PhysRevLett.126.174102⟩. ⟨hal-02987847⟩We present an extension of the chaos-tunneling mechanism to spatially periodic lattice systems. We demonstrate that driving such lattice systems in an intermediate regime of modulation maps them onto tight-binding Hamiltonians with chaos-induced long-range hoppings tn ∝ 1/n between sites at a distance n. We provide numerical demonstration of the robustness of the results and derive an analytical prediction for the hopping term law. Such systems can thus be used to enlarge the scope of quantum simulations in order to experimentally realize long-range models of condensed matter.

- 1. LPT - Laboratoire de Physique Théorique
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. LCAR - Laboratoire Collisions Agrégats Réactivité
- 4. UMI 3654 - MajuLab
- 5. CQT - Centre for Quantum Technologies [Singapore]

## Constrained non-crossing Brownian motions, fermions and the Ferrari–Spohn distribution – Archive ouverte HAL

### Tristan Gautié

^{1}Naftali R. Smith^{2, 1}#### Tristan Gautié, Naftali R. Smith. Constrained non-crossing Brownian motions, fermions and the Ferrari–Spohn distribution.

*J.Stat.Mech.*, 2021, 2103, pp.033212. ⟨10.1088/1742-5468/abe59c⟩. ⟨hal-03186169⟩A conditioned stochastic process can display a very different behavior from the unconditioned process. In particular, a conditioned process can exhibit non-Gaussian fluctuations even if the unconditioned process is Gaussian. In this work, we revisit the Ferrari–Spohn model of a Brownian bridge conditioned to avoid a moving wall, which pushes the system into a large-deviation regime. We extend this model to an arbitrary number N of non-crossing Brownian bridges. We obtain the joint distribution of the distances of the Brownian particles from the wall at an intermediate time in the form of the determinant of an N × N matrix whose entries are given in terms of the Airy function. We show that this distribution coincides with that of the positions of N spinless noninteracting fermions trapped by a linear potential with a hard wall. We then explore the N ≫ 1 behavior of the system. For simplicity we focus on the case where the wall’s position is given by a semicircle as a function of time, but we expect our results to be valid for any concave wall function.

- 1. Champs Aléatoires et Systèmes hors d'Équilibre
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Counting statistics for noninteracting fermions in a d -dimensional potential – Archive ouverte HAL

### Naftali R. Smith

^{1}Pierre Le Doussal^{2}Satya N. Majumdar^{3}Grégory Schehr^{3}#### Naftali R. Smith, Pierre Le Doussal, Satya N. Majumdar, Grégory Schehr. Counting statistics for noninteracting fermions in a d -dimensional potential.

*Physical Review E*, American Physical Society (APS), 2021, 103 (3), ⟨10.1103/PhysRevE.103.L030105⟩. ⟨hal-03179783⟩We develop a first-principle approach to compute the counting statistics in the ground-state of $N$ noninteracting spinless fermions in a general potential in arbitrary dimensions $d$ (central for $d>1$). In a confining potential, the Fermi gas is supported over a bounded domain. In $d=1$, for specific potentials, this system is related to standard random matrix ensembles. We study the quantum fluctuations of the number of fermions ${\cal N}_{\cal D}$ in a domain $\cal{D}$ of macroscopic size in the bulk of the support. We show that the variance of ${\cal N}_{\cal D}$ grows as $N^{(d-1)/d} (A_d \log N + B_d)$ for large $N$, and obtain the explicit dependence of $A_d, B_d$ on the potential and on the size of ${\cal D}$ (for a spherical domain in $d>1$). This generalizes the free-fermion results for microscopic domains, given in $d=1$ by the Dyson-Mehta asymptotics from random matrix theory. This leads us to conjecture similar asymptotics for the entanglement entropy of the subsystem $\cal{D}$, in any dimension, supported by exact results for $d=1$.

- 1. LPMS - Laboratoire de Physique des Matériaux et des Surfaces
- 2. Champs Aléatoires et Systèmes hors d'Équilibre
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Dynamical instantons and activated processes in mean-field glass models – Archive ouverte HAL

### Valentina Ros

^{1, 2}Giulio Biroli^{2}Chiara Cammarota#### Valentina Ros, Giulio Biroli, Chiara Cammarota. Dynamical instantons and activated processes in mean-field glass models.

*SciPost Physics*, SciPost Foundation, 2021, 10 (1), ⟨10.21468/SciPostPhys.10.1.002⟩. ⟨hal-03118004⟩We focus on the energy landscape of a simple mean-field model of glasses and analyze activated barrier-crossing by combining the Kac-Rice method for high-dimensional Gaussian landscapes with dynamical field theory. In particular, we consider Langevin dynamics at low temperature in the energy landscape of the pure spherical $p$-spin model. We select as initial condition for the dynamics one of the many unstable index-1 saddles in the vicinity of a reference local minimum. We show that the associated dynamical mean-field equations admit two solutions: one corresponds to falling back to the original reference minimum, and the other to reaching a new minimum past the barrier. By varying the saddle we scan and characterize the properties of such minima reachable by activated barrier-crossing. Finally, using time-reversal transformations, we construct the two-point function dynamical instanton of the corresponding activated process.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Systèmes Désordonnés et Applications

## Electroosmosis as a probe for electrostatic correlations – Archive ouverte HAL

### Ivan PalaiaIgor M. TellesAlexandre P. Dos SantosEmmanuel Trizac

^{1}#### Ivan Palaia, Igor M. Telles, Alexandre P. Dos Santos, Emmanuel Trizac. Electroosmosis as a probe for electrostatic correlations.

*Soft Matter*, Royal Society of Chemistry, 2021. ⟨hal-03223905⟩We study the role of ionic correlations on the electroosmotic flow in planar double-slit channels, without salt. We propose an analytical theory, based on recent advances in the understanding of correlated systems. We compare the theory with mean-field results and validate it by means of dissipative particle dynamics simulations. Interestingly, for some surface separations, correlated systems exhibit a larger flow than predicted by mean-field. We conclude that the electroosmotic properties of a charged system can be used, in general, to infer and weight the importance of electrostatic correlations therein.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Formation of superscar waves in plane polygonal billiards – Archive ouverte HAL

### Eugene Bogomolny

^{1}#### Eugene Bogomolny. Formation of superscar waves in plane polygonal billiards.

*Journal of Physics Communications*, IOP Publishing, 2021. ⟨hal-03262543⟩Polygonal billiards constitute a special class of models. Though they have zero Lyapunov exponent their classical and quantum properties are involved due to scattering on singular vertices. It is demonstrated that in the semiclassical limit multiple singular scattering on such vertices when optical boundaries of many scatters overlap leads to vanishing of quantum wave functions along straight lines built by these scatters. This phenomenon has an especially important consequence for polygonal billiards where periodic orbits (when they exist) form pencils of parallel rays restricted from the both sides by singular vertices. Due to singular scattering on boundary vertices, waves propagated inside periodic orbit pencils in the semiclassical limit tend to zero along pencil boundaries thus forming weakly interacting quasi-modes. Contrary to scars in chaotic systems the discussed quasi-modes in polygonal billiards become almost exact for high-excited states and for brevity they are designated as superscars. Many pictures of eigenfunctions for a triangular billiard and a barrier billiard which have clear superscar structures are presented in the paper. Special attention is given to the development of quantitative methods of detecting and analysing such superscars. In particular, it is demonstrated that the overlap between superscar waves associated with a fixed periodic orbit and eigenfunctions of a barrier billiard is distributed according to the Breit-Wigner distribution typical for weakly interacting quasi-modes (or doorway states). For special sub-class of rational polygonal billiards called Veech polygons where all periodic orbits can be calculated analytically it is argued and checked numerically that their eigenfunctions are fractal in the Fourier space.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## From One- to Two-Magnon Excitations in the S = 3 / 2 Magnet β − CaCr 2 O 4 – Archive ouverte HAL

### M. SongvilayS. PetitF. DamayG. Roux

^{1}N. QureshiH. c. WalkerJ. a. Rodriguez-RiveraB. GaoS. -W. CheongC. Stock#### M. Songvilay, S. Petit, F. Damay, G. Roux, N. Qureshi, et al.. From One- to Two-Magnon Excitations in the S = 3 / 2 Magnet β − CaCr 2 O 4.

*Physical Review Letters*, American Physical Society, 2021, 126 (1), ⟨10.1103/PhysRevLett.126.017201⟩. ⟨hal-03117938⟩We apply neutron spectroscopy to measure the magnetic dynamics in the S=3/2 magnet $\beta$-CaCr$_2$O$_4$ (T$_N$=21 K). The low-energy fluctuations, in the ordered state, resemble large-S linear spin-waves from the incommensurate ground state. However, at higher energy transfers, these semi-classical and harmonic dynamics are replaced by an energy and momentum broadened continuum of excitations. Applying kinematic constraints required for energy and momentum conservation, sum rules of neutron scattering, and comparison against exact diagonalization calculations, we show that the dynamics at high-energy transfers resemble low-S one-dimensional quantum fluctuations. $\beta$-CaCr$_2$O$_4$ represents an example of a magnet at the border between classical N\'eel and quantum phases, displaying dual characteristics.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Gradient descent dynamics in the mixed $p$-spin spherical model: finite size simulation and comparison with mean-field integration – Archive ouverte HAL

### Giampaolo Folena

^{1}Silvio Franz^{1}Federico Ricci-Tersenghi#### Giampaolo Folena, Silvio Franz, Federico Ricci-Tersenghi. Gradient descent dynamics in the mixed $p$-spin spherical model: finite size simulation and comparison with mean-field integration.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2021. ⟨hal-03223872⟩We perform numerical simulations of a long-range spherical spin glass with two and three body interaction terms. We study the gradient descent dynamics and the inherent structures found after a quench from initial conditions, well thermalized at temperature $T_{in}$. In large systems, the dynamics strictly agrees with the integration of the mean-field dynamical equations. In particular, we confirm the existence of an onset initial temperature, within the liquid phase, below which the energy of the inherent structures undoubtedly depends on $T_{in}$. This behavior is in contrast with that of pure models, where there is a 'threshold energy' that attracts all the initial configurations in the liquid. Our results strengthen the analogy between mean-field spin glass models and supercooled liquids.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Higher-order effective interactions for bosons near a two-body zero crossing – Archive ouverte HAL

### A. Pricoupenko

^{1}D. S. Petrov^{1}#### A. Pricoupenko, D. S. Petrov. Higher-order effective interactions for bosons near a two-body zero crossing.

*Physical Review A*, American Physical Society 2021, 103 (3), ⟨10.1103/PhysRevA.103.033326⟩. ⟨hal-03223944⟩We develop the perturbation theory for bosons interacting via a two-body potential $V$ of vanishing mean value. We find that the leading nonpairwise contribution to the energy emerges in the third order in $V$ and represents an effective three-body interaction, the sign of which in most cases (although not in general) is anticorrelated with the sign of the long-range tail of $V$. Explicit results are obtained for a few particular two-body interaction potentials and we perform a detailed perturbative analysis of tilted dipoles in quasi-low-dimensional geometries.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Impurities in systems of noninteracting trapped fermions – Archive ouverte HAL

### David S. Dean

^{1}Pierre Le Doussal^{2}Satya N. Majumdar^{3}Gregory Schehr^{3}#### David S. Dean, Pierre Le Doussal, Satya N. Majumdar, Gregory Schehr. Impurities in systems of noninteracting trapped fermions.

*SciPost Physics*, SciPost Foundation, 2021, 10 (4), ⟨10.21468/SciPostPhys.10.4.082⟩. ⟨hal-03223977⟩We study the properties of spin-less non-interacting fermions trapped in a confining potential in one dimension but in the presence of one or more impurities which are modelled by delta function potentials. We use a method based on the single particle Green's function. For a single impurity placed in the bulk, we compute the density of the Fermi gas near the impurity. Our results, in addition to recovering the Friedel oscillations at large distance from the impurity, allow the exact computation of the density at short distances. We also show how the density of the Fermi gas is modified when the impurity is placed near the edge of the trap in the region where the unperturbed system is described by the Airy gas. Our method also allows us to compute the effective potential felt by the impurity both in the bulk and at the edge. In the bulk this effective potential is shown to be a universal function only of the local Fermi wave vector, or equivalently of the local fermion density. When the impurity is placed near the edge of the Fermi gas, the effective potential can be expressed in terms of Airy functions. For an attractive impurity placed far outside the support of the fermion density, we show that an interesting transition occurs where a single fermion is pulled out of the Fermi sea and forms a bound state with the impurity. This is a quantum analogue of the well-known Baik-Ben Arous-Péché (BBP) transition, known in the theory of spiked random matrices. The density at the location of the impurity plays the role of an order parameter. We also consider the case of two impurities in the bulk and compute exactly the effective force between them mediated by the background Fermi gas.

- 1. LOMA - Laboratoire Ondes et Matière d'Aquitaine
- 2. LPENS (UMR_8023) - Laboratoire de physique de l'ENS - ENS Paris
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Kernels for non interacting fermions via a Green’s function approach with applications to step potentials – Archive ouverte HAL

### Pierre Le Doussal

^{1}Satya N. Majumdar^{2}Grégory Schehr^{2}Naftali R. Smith^{2}David Dean^{3}#### Pierre Le Doussal, Satya N. Majumdar, Grégory Schehr, Naftali R. Smith, David Dean. Kernels for non interacting fermions via a Green’s function approach with applications to step potentials.

*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2021, 54 (8), pp.084001. ⟨10.1088/1751-8121/abd9ef⟩. ⟨hal-03177657⟩The quantum correlations of $N$ noninteracting spinless fermions in their ground state can be expressed in terms of a two-point function called the kernel. Here we develop a general and compact method for computing the kernel in a general trapping potential in terms of the Green's function for the corresponding single particle Schr\"odinger equation. For smooth potentials the method allows a simple alternative derivation of the local density approximation for the density and of the sine kernel in the bulk part of the trap in the large $N$ limit. It also recovers the density and the kernel of the so-called {\em Airy gas} at the edge. This method allows to analyse the quantum correlations in the ground state when the potential has a singular part with a fast variation in space. For the square step barrier of height $V_0$, we derive explicit expressions for the density and for the kernel. For large Fermi energy $\mu>V_0$ it describes the interpolation between two regions of different densities in a Fermi gas, each described by a different sine kernel. Of particular interest is the {\em critical point} of the square well potential when $\mu=V_0$. In this critical case, while there is a macroscopic number of fermions in the lower part of the step potential, there is only a finite $O(1)$ number of fermions on the shoulder, and moreover this number is independent of $\mu$. In particular, the density exhibits an algebraic decay $\sim 1/x^2$, where $x$ is the distance from the jump. Furthermore, we show that the critical behaviour around $\mu = V_0$ exhibits universality with respect with the shape of the barrier. This is established (i) by an exact solution for a smooth barrier (the Woods-Saxon potential) and (ii) by establishing a general relation between the large distance behavior of the kernel and the scattering amplitudes of the single-particle wave-function.

- 1. Champs Aléatoires et Systèmes hors d'Équilibre
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. LOMA - Laboratoire Ondes et Matière d'Aquitaine

## Level Set Percolation in the Two-Dimensional Gaussian Free Field – Archive ouverte HAL

### Xiangyu Cao

^{1}Raoul Santachiara^{2}#### Xiangyu Cao, Raoul Santachiara. Level Set Percolation in the Two-Dimensional Gaussian Free Field.

*Physical Review Letters*, American Physical Society, 2021, 126 (12), ⟨10.1103/PhysRevLett.126.120601⟩. ⟨hal-03176908⟩- 1. Systèmes Classiques ou Quantiques en Interaction
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Localization transition in the Discrete Non-Linear Schr\ »odinger Equation: ensembles inequivalence and negative temperatures – Archive ouverte HAL

### Giacomo GradenigoStefano IubiniRoberto LiviSatya N. Majumdar

^{1}#### Giacomo Gradenigo, Stefano Iubini, Roberto Livi, Satya N. Majumdar. Localization transition in the Discrete Non-Linear Schr\"odinger Equation: ensembles inequivalence and negative temperatures.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2021. ⟨hal-03223864⟩We present a detailed account of a first-order localization transition in the Discrete Nonlinear Schr\"odinger Equation, where the localized phase is associated to the high energy region in parameter space. We show that, due to ensemble inequivalence, this phase is thermodynamically stable only in the microcanonical ensemble. In particular, we obtain an explicit expression of the microcanonical entropy close to the transition line, located at infinite temperature. This task is accomplished making use of large-deviation techniques, that allow us to compute, in the limit of large system size, also the subleading corrections to the microcanonical entropy. These subleading terms are crucial ingredients to account for the first-order mechanism of the transition, to compute its order parameter and to predict the existence of negative temperatures in the localized phase. All of these features can be viewed as signatures of a thermodynamic phase where the translational symmetry is broken spontaneously due to a condensation mechanism yielding energy fluctuations far away from equipartition: actually they prefer to participate in the formation of nonlinear localized excitations (breathers), typically containing a macroscopic fraction of the total energy.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Mean perimeter and area of the convex hull of a planar Brownian motion in the presence of resetting – Archive ouverte HAL

### Satya N. Majumdar

^{1}Francesco Mori^{1}Hendrik Schawe^{2}Grégory Schehr^{1}#### Satya N. Majumdar, Francesco Mori, Hendrik Schawe, Grégory Schehr. Mean perimeter and area of the convex hull of a planar Brownian motion in the presence of resetting.

*Physical Review E*, American Physical Society (APS), 2021, 103 (2), ⟨10.1103/PhysRevE.103.022135⟩. ⟨hal-03177642⟩We compute exactly the mean perimeter and the mean area of the convex hull of a $2$-d Brownian motion of duration $t$ and diffusion constant $D$, in the presence of resetting to the origin at a constant rate $r$. We show that for any $t$, the mean perimeter is given by $\langle L(t)\rangle= 2 \pi \sqrt{\frac{D}{r}}\, f_1(rt)$ and the mean area is given by $\langle A(t) \rangle= 2\pi\frac{D}{r}\, f_2(rt)$ where the scaling functions $f_1(z)$ and $f_2(z)$ are computed explicitly. For large $t\gg 1/r$, the mean perimeter grows extremely slowly as $\langle L(t)\rangle \propto \ln (rt)$ with time. Likewise, the mean area also grows slowly as $\langle A(t)\rangle \propto \ln^2(rt)$ for $t\gg 1/r$. Our exact results indicate that the convex hull, in the presence of resetting, approaches a circular shape at late times. Numerical simulations are in perfect agreement with our analytical predictions.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTM - UMR 8089 - Laboratoire de Physique Théorique et Modélisation

## Mixed Bubbles in Bose-Bose Mixtures – Archive ouverte HAL

### P. NaidonD. s. Petrov

^{1}#### P. Naidon, D. s. Petrov. Mixed Bubbles in Bose-Bose Mixtures.

*Physical Review Letters*, American Physical Society, 2021, 126 (11), ⟨10.1103/PhysRevLett.126.115301⟩. ⟨hal-03223902⟩Repulsive Bose-Bose mixtures are known to either mix or phase-separate into pure components. Here we predict a mixed-bubble regime in which bubbles of the mixed phase coexist with a pure phase of one of the components. This is a beyond-mean-field effect which occurs for unequal masses or unequal intraspecies coupling constants and is due to a competition between the mean-field term, quadratic in densities, and a nonquadratic beyond-mean-field correction. We find parameters of the mixed-bubble regime in all dimensions and discuss implications for current experiments.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Multilayered density profile for noninteracting fermions in a rotating two-dimensional trap – Archive ouverte HAL

### Manas Kulkarni

^{1}Satya N. Majumdar^{2}Grégory Schehr^{2}#### Manas Kulkarni, Satya N. Majumdar, Grégory Schehr. Multilayered density profile for noninteracting fermions in a rotating two-dimensional trap.

*Physical Review A*, American Physical Society 2021, 103 (3), ⟨10.1103/PhysRevA.103.033321⟩. ⟨hal-03179775⟩We compute exactly the average spatial density for $N$ spinless noninteracting fermions in a $2d$ harmonic trap rotating with a constant frequency $\Omega$ in the presence of an additional repulsive central potential $\gamma/r^2$. We find that, in the large $N$ limit, the bulk density has a rich and nontrivial profile -- with a hole at the center of the trap and surrounded by a multi-layered "wedding cake" structure. The number of layers depends on $N$ and on the two parameters $\Omega$ and $\gamma$ leading to a rich phase diagram. Zooming in on the edge of the $k^{\rm th}$ layer, we find that the edge density profile exhibits $k$ kinks located at the zeroes of the $k^{\rm th}$ Hermite polynomial. Interestingly, in the large $k$ limit, we show that the edge density profile approaches a limiting form, which resembles the shape of a propagating front, found in the unitary evolution of certain quantum spin chains. We also study how a newly formed droplet grows in size on top of the last layer as one changes the parameters.

- 1. ICTS-TIFR - International Centre for Theoretical Sciences [TIFR]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Neutral theory for competing attention in social networks – Archive ouverte HAL

### Carlos A. Plata

^{1, 2}Emanuele Pigani^{2}Sandro Azaele^{2}María J. PalazziAlbert Solé-RibaltaSandro MeloniJavier Borge-HolthoeferSamir Suweis^{2}Violeta Calleja-Solanas#### Carlos A. Plata, Emanuele Pigani, Sandro Azaele, María J. Palazzi, Albert Solé-Ribalta, et al.. Neutral theory for competing attention in social networks.

*Physical Review Research*, American Physical Society, 2021, 3 (1), ⟨10.1103/PhysRevResearch.3.013070⟩. ⟨hal-03180557⟩We used an ecological approach based on a neutral model to study the competition for attention in an online social network. This novel approach allow us to analyze some ecological patterns that has also an insightful meaning in the context of information ecosystem. Specifically, we focus on the study of patterns related with the persistence of a meme within the network and the capacity of the system to sustain coexisting memes. Not only are we able of doing such analysis in an approximated continuum limit, but also we get exact results of the finite-size discrete system.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Dipartimento di Fisica [Padova]

## Non-canonical degrees of freedom – Archive ouverte HAL

### Eoin Quinn

^{1}#### Eoin Quinn. Non-canonical degrees of freedom.

*SciPost Phys.*, 2021, 10, pp.075. ⟨10.21468/SciPostPhys.10.3.075⟩. ⟨hal-02973159⟩Non-canonical degrees of freedom provide one of the most promising routes towards characterising a range of important phenomena in condensed matter physics. Potential candidates include the pseudogap regime of the cuprates, heavy-fermion behaviour, and also indeed magnetically ordered systems. Nevertheless it remains an open question whether non-canonical algebras can in fact provide legitimate quantum degrees of freedom. In this manuscript we survey progress made on this topic, complementing distinct approaches so as to obtain a unified description. In particular we obtain a novel closed-form expression for a self-energy-like object for non-canonical degrees of freedom. We further make a resummation of density correlations to obtain analogues of the RPA and GW approximations commonly employed for canonical degrees of freedom. We discuss difficulties related to generating higher-order approximations which are consistent with conservation laws, which represents an outstanding issue. We also discuss how the interplay between canonical and non-canonical degrees of freedom offers a useful paradigm for organising the phase diagram of correlated electronic behaviour.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Non-intersecting Brownian Bridges in the Flat-to-Flat Geometry – Archive ouverte HAL

### Jacek GrelaSatya N. Majumdar

^{1}Grégory Schehr^{2}#### Jacek Grela, Satya N. Majumdar, Grégory Schehr. Non-intersecting Brownian Bridges in the Flat-to-Flat Geometry.

*J.Statist.Phys.*, 2021, 183 (3), pp.49. ⟨10.1007/s10955-021-02774-6⟩. ⟨hal-03260827⟩We study N vicious Brownian bridges propagating from an initial configuration $\{a_1< a_2< \ldots < a_N \}$ at time $t=0$ to a final configuration $\{b_1< b_2< \ldots < b_N \}$ at time $t=t_f$, while staying non-intersecting for all $0\le t \le t_f$. We first show that this problem can be mapped to a non-intersecting Dyson’s Brownian bridges with Dyson index $\beta =2$. For the latter we derive an exact effective Langevin equation that allows to generate very efficiently the vicious bridge configurations. In particular, for the flat-to-flat configuration in the large N limit, where $a_i = b_i = (i-1)/N$, for $i = 1, \ldots , N$, we use this effective Langevin equation to derive an exact Burgers’ equation (in the inviscid limit) for the Green’s function and solve this Burgers’ equation for arbitrary time $0 \le t\le t_f$. At certain specific values of intermediate times t, such as $t=t_f/2$, $t=t_f/3$ and $t=t_f/4$ we obtain the average density of the flat-to-flat bridge explicitly. We also derive explicitly how the two edges of the average density evolve from time $t=0$ to time $t=t_f$. Finally, we discuss connections to some well known problems, such as the Chern–Simons model, the related Stieltjes–Wigert orthogonal polynomials and the Borodin–Muttalib ensemble of determinantal point processes.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTHE - Laboratoire de Physique Théorique et Hautes Energies

## On non-canonical degrees of freedom – Archive ouverte HAL

### Eoin Quinn

^{1}#### Eoin Quinn. On non-canonical degrees of freedom.

*SciPost Phys.*, 2021, 10, pp.075. ⟨10.21468/SciPostPhys.10.3.075⟩. ⟨hal-02973159⟩Non-canonical degrees of freedom provide one of the most promising routes towards characterising a range of important phenomena in condensed matter physics. Potential candidates include the pseudogap regime of the cuprates, heavy-fermion behaviour, and also indeed magnetically ordered systems. Nevertheless it remains an open question whether non-canonical algebras can in fact provide legitimate quantum degrees of freedom. In this manuscript we survey progress made on this topic, complementing distinct approaches so as to obtain a unified description. In particular we obtain a novel closed-form expression for a self-energy-like object for non-canonical degrees of freedom. We further make a resummation of density correlations to obtain analogues of the RPA and GW approximations commonly employed for canonical degrees of freedom. We discuss difficulties related to generating higher-order approximations which are consistent with conservation laws, which represents an outstanding issue. We also discuss how the interplay between canonical and non-canonical degrees of freedom offers a useful paradigm for organising the phase diagram of correlated electronic behaviour.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## One-dimensional colloidal model with dielectric inhomogeneity – Archive ouverte HAL

### Lucas Varela

^{1}Gabriel TéllezEmmanuel Trizac^{1}#### Lucas Varela, Gabriel Téllez, Emmanuel Trizac. One-dimensional colloidal model with dielectric inhomogeneity.

*Physical Review E*, American Physical Society (APS), 2021, 103 (4), ⟨10.1103/PhysRevE.103.042603⟩. ⟨hal-03223979⟩We consider a one-dimensional model allowing analytical derivation of the effective interactions between two charged colloids. We evaluate exactly the partition function for an electroneutral salt-free suspension with dielectric jumps at the colloids' position. We derive a contact relation with the pressure that shows there is like-charge attraction, whether or not the counterions are confined between the colloids. In contrast to the homogeneous dielectric case, there is the possibility for the colloids to attract despite the number of counter-ions ($N$) being even. The results are shown to recover the mean-field prediction in the limit $N\to \infty$.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Optimization and Growth in First-Passage Resetting – Archive ouverte HAL

### B. de Bruyne

^{1}J. Randon-FurlingS. Redner#### B. de Bruyne, J. Randon-Furling, S. Redner. Optimization and Growth in First-Passage Resetting.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2021. ⟨hal-03117919⟩We combine the processes of resetting and first-passage to define \emph{first-passage resetting}, where the resetting of a random walk to a fixed position is triggered by a first-passage event of the walk itself. In an infinite domain, first-passage resetting of isotropic diffusion is non-stationary, with the number of resetting events growing with time as $\sqrt{t}$. We calculate the resulting spatial probability distribution of the particle analytically, and also obtain this distribution by a geometric path decomposition. In a finite interval, we define an optimization problem that is controlled by first-passage resetting; this scenario is motivated by reliability theory. The goal is to operate a system close to its maximum capacity without experiencing too many breakdowns. However, when a breakdown occurs the system is reset to its minimal operating point. We define and optimize an objective function that maximizes the reward (being close to maximum operation) minus a penalty for each breakdown. We also investigate extensions of this basic model to include delay after each reset and to two dimensions. Finally, we study the growth dynamics of a domain in which the domain boundary recedes by a specified amount whenever the diffusing particle reaches the boundary after which a resetting event occurs. We determine the growth rate of the domain for the semi-infinite line and the finite interval and find a wide range of behaviors that depend on how much the recession occurs when the particle hits the boundary.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Pairing in spinless fermions and spin chains with next-nearest neighbor interactions – Archive ouverte HAL

### Lorenzo Gotta

^{1}Leonardo Mazza^{1}Pascal Simon^{2}Guillaume Roux^{1}#### Lorenzo Gotta, Leonardo Mazza, Pascal Simon, Guillaume Roux. Pairing in spinless fermions and spin chains with next-nearest neighbor interactions.

*Physical Review Research*, American Physical Society, 2021, 3 (1), ⟨10.1103/PhysRevResearch.3.013114⟩. ⟨hal-03177638⟩We investigate the phase diagrams of a one-dimensional lattice model of fermions and of a spin chain with interactions extending up to next-nearest neighbour range. In particular, we investigate the appearance of regions with dominant pairing physics in the presence of nearest-neighbour and next-nearest-neighbour interactions. Our analysis is based on analytical calculations in the classical limit, bosonization techniques and large-scale density-matrix renormalization group numerical simulations. The phase diagram, which is investigated in all relevant filling regimes, displays a remarkably rich collection of phases, including Luttinger liquids, phase separation, charge-density waves, bond-order phases, and exotic cluster Luttinger liquids with paired particles. In relation with recent studies, we show several emergent transition lines with a central charge $c = 3/2$ between the Luttinger-liquid and the cluster Luttinger liquid phases. These results could be experimentally investigated using highly-tunable quantum simulators.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPS - Laboratoire de Physique des Solides

## Phase slips, dislocations, half-integer vortices, two-fluid hydrodynamics and the chiral anomaly in charge and spin density waves – Archive ouverte HAL

### Serguei Brazovskii

^{1}Natasha Kirova^{2}#### Serguei Brazovskii, Natasha Kirova. Phase slips, dislocations, half-integer vortices, two-fluid hydrodynamics and the chiral anomaly in charge and spin density waves.

*J.Exp.Theor.Phys.*, 2021, 132 (4), pp.714-726. ⟨10.1134/S1063776121040038⟩. ⟨hal-03178611⟩This brief review recalls some chapters in theory of sliding incommensurate density waves which may have appeared after inspirations from studies of Dzyaloshinskii and collaborations with him. First we address the spin density waves which rich order parameter allows for an unusual object of a complex topological nature: a half-integer dislocation combined with a semi-vortex of the staggered magnetization. It becomes energetically preferable with respect to an ordinary dislocation due to the high Coulomb energy at low concentration of carriers. Generation of these objects should form a sequence of π-phase slips in accordance with experimental doubling of the phase-slips rate. Next, we revise the commonly employed TDGL approach which is shown to suffer from a violation of the charge conservation law resulting in nonphysical generation of particles which is particularly pronounced for electronic vortices in the course of their nucleation or motion. The suggested consistent theory exploits the chiral transformations taking into account the principle contribution of the fermionic chiral anomaly to the effective action. The derived equations clarify partitions of charges, currents, and rigidity among subsystems of condensed and normal carriers and the gluing electric field. Being non-analytical with respect to the order parameter, contrarily the conventional TDGL type, the resulting equations still allow for a numerical modeling of transient processes related to space- and spatiotemporal vorticity in DWs.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPS - Laboratoire de Physique des Solides

## Position distribution in a generalized run-and-tumble process – Archive ouverte HAL

### David S. Dean

^{1}Satya N. Majumdar^{2}Hendrik Schawe#### David S. Dean, Satya N. Majumdar, Hendrik Schawe. Position distribution in a generalized run-and-tumble process.

*Physical Review E*, American Physical Society (APS), 2021, 103 (1), ⟨10.1103/PhysRevE.103.012130⟩. ⟨hal-03223889⟩We study a class of stochastic processes of the type $\frac{d^n x}{dt^n}= v_0\, \sigma(t)$ where $n>0$ is a positive integer and $\sigma(t)=\pm 1$ represents an `active' telegraphic noise that flips from one state to the other with a constant rate $\gamma$. For $n=1$, it reduces to the standard run and tumble process for active particles in one dimension. This process can be analytically continued to any $n>0$ including non-integer values. We compute exactly the mean squared displacement at time $t$ for all $n>0$ and show that at late times while it grows as $\sim t^{2n-1}$ for $n>1/2$, it approaches a constant for $n<1/2$. In the marginal case $n=1/2$, it grows very slowly with time as $\sim \ln t$. Thus the process undergoes a {\em localisation} transition at $n=1/2$. We also show that the position distribution $p_n(x,t)$ remains time-dependent even at late times for $n\ge 1/2$, but approaches a stationary time-independent form for $n<1/2$. The tails of the position distribution at late times exhibit a large deviation form, $p_n(x,t)\sim \exp\left[-\gamma\, t\, \Phi_n\left(\frac{x}{x^*(t)}\right)\right]$, where $x^*(t)= v_0\, t^n/\Gamma(n+1)$. We compute the rate function $\Phi_n(z)$ analytically for all $n>0$ and also numerically using importance sampling methods, finding excellent agreement between them. For three special values $n=1$, $n=2$ and $n=1/2$ we compute the exact cumulant generating function of the position distribution at all times $t$.

- 1. LOMA - Laboratoire Ondes et Matière d'Aquitaine
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Proliferation of non-linear excitations in the piecewise-linear perceptron – Archive ouverte HAL

### Antonio Sclocchi

^{1}Pierfrancesco Urbani^{2}#### Antonio Sclocchi, Pierfrancesco Urbani. Proliferation of non-linear excitations in the piecewise-linear perceptron.

*SciPost Physics*, SciPost Foundation, 2021. ⟨hal-03223926⟩We investigate the properties of local minima of the energy landscape of a continuous non-convex optimization problem, the spherical perceptron with piecewise linear cost function and show that they are critical, marginally stable and displaying a set of pseudogaps, singularities and non-linear excitations whose properties appear to be in the same universality class of jammed packings of hard spheres. The piecewise linear perceptron problem appears as an evolution of the purely linear perceptron optimization problem that has been recently investigated in [1]. Its cost function contains two non-analytic points where the derivative has a jump. Correspondingly, in the non-convex/glassy phase, these two points give rise to four pseudogaps in the force distribution and this induces four power laws in the gap distribution as well. In addition one can define an extended notion of isostaticity and show that local minima appear again to be isostatic in this phase. We believe that our results generalize naturally to more complex cases with a proliferation of non-linear excitations as the number of non-analytic points in the cost function is increased.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. IPHT - Institut de Physique Théorique - UMR CNRS 3681

## Self-induced glassy phase in multimodal cavity quantum electrodynamics – Archive ouverte HAL

### Vittorio ErbaMauro Pastore

^{1}Pietro Rotondo#### Vittorio Erba, Mauro Pastore, Pietro Rotondo. Self-induced glassy phase in multimodal cavity quantum electrodynamics.

*Physical Review Letters*, American Physical Society, 2021. ⟨hal-03223947⟩We provide strong evidence that the effective spin-spin interaction in a multimodal confocal optical cavity gives rise to a self-induced glassy phase, which emerges exclusively from the peculiar euclidean correlations and is not related to the presence of disorder as in standard spin glasses. As recently shown, this spin-spin effective interaction is both non-local and non-translational invariant, and randomness in the atoms positions produces a spin glass phase. Here we consider the simplest feasible disorder-free setting where atoms form a one-dimensional regular chain and we study the thermodynamics of the resulting effective Ising model. We present extensive results showing that the system has a low-temperature glassy phase. Notably, for rational values of the only free adimensional parameter $\alpha=p/q$ of the interaction, the number of metastable states at low temperature grows exponentially with $q$ and the problem of finding the ground state rapidly becomes computationally intractable, suggesting that the system develops high energy barriers and ergodicity breaking occurs.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Spatial Clustering of Depinning Avalanches in Presence of Long-Range Interactions – Archive ouverte HAL

### Clément Le PriolPierre Le Doussal

^{1}Alberto Rosso^{2}#### Clément Le Priol, Pierre Le Doussal, Alberto Rosso. Spatial Clustering of Depinning Avalanches in Presence of Long-Range Interactions.

*Physical Review Letters*, American Physical Society, 2021, 126 (2), ⟨10.1103/PhysRevLett.126.025702⟩. ⟨hal-03117974⟩Disordered elastic interfaces display avalanche dynamics at the depinning transition. For short-range interactions, avalanches correspond to compact reorganizations of the interface well described by the depinning theory. For long-range elasticity, an avalanche is a collection of spatially disconnected clusters. In this paper we determine the scaling properties of the clusters and relate them to the roughness exponent of the interface. The key observation of our analysis is the identification of a Bienaym{\'e}-Galton-Watson process describing the statistics of the cluster number. Our work has a concrete importance for experimental applications where the cluster statistics is a key probe of avalanche dynamics.

- 1. Champs Aléatoires et Systèmes hors d'Équilibre
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Statistical properties of structured random matrices – Archive ouverte HAL

### Eugene Bogomolny

^{1}Olivier Giraud^{1}#### Eugene Bogomolny, Olivier Giraud. Statistical properties of structured random matrices.

*Physical Review E*, American Physical Society (APS), 2021, 103 (4), ⟨10.1103/PhysRevE.103.042213⟩. ⟨hal-03223965⟩Spectral properties of Hermitian Toeplitz, Hankel, and Toeplitz-plus-Hankel random matrices with independent identically distributed entries are investigated. Combining numerical and analytic arguments it is demonstrated that spectral statistics of all these random matrices is of intermediate type, characterized by (i) level repulsion at small distances, (ii) an exponential decrease of the nearest-neighbor distributions at large distances, (iii) a non-trivial value of the spectral compressibility, and (iv) the existence of non-trivial fractal dimensions of eigenvectors in Fourier space. Our findings show that intermediate-type statistics is more ubiquitous and universal than was considered so far and open a new direction in random matrix theory.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Supersolidity of cnoidal waves in an ultracold Bose gas – Archive ouverte HAL

### Giovanni I. MartoneAlessio RecatiNicolas Pavloff

^{1}#### Giovanni I. Martone, Alessio Recati, Nicolas Pavloff. Supersolidity of cnoidal waves in an ultracold Bose gas.

*Physical Review Research*, American Physical Society, 2021, 3 (1), ⟨10.1103/PhysRevResearch.3.013143⟩. ⟨hal-03223891⟩A one-dimensional Bose-Einstein condensate may experience nonlinear periodic modulations known as "cnoidal waves". We argue that such structures represent promising candidates for the study of supersolidity-related phenomena in a non-equilibrium state. A mean-field treatment makes it possible to rederive Leggett's formula for the superfluid fraction of the system and to estimate it analytically. We determine the excitation spectrum, for which we obtain analytical results in the two opposite limiting cases of (i) a linearly modulated background and (ii) a train of dark solitons. The presence of two Goldstone (gapless) modes -- associated with the spontaneous breaking of $\mathrm{U}(1)$ symmetry and of continuous translational invariance -- at large wavelength is verified. We also calculate the static structure factor and the compressibility of cnoidal waves, which show a divergent behavior at the edges of each Brillouin zone.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Surfing on minima of isostatic landscapes: avalanches and unjamming transition – Archive ouverte HAL

### Silvio Franz

^{1}Antonio Sclocchi^{1}Pierfrancesco Urbani^{2}#### Silvio Franz, Antonio Sclocchi, Pierfrancesco Urbani. Surfing on minima of isostatic landscapes: avalanches and unjamming transition.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2021. ⟨hal-03223882⟩Recently, we showed that optimization problems, both in infinite as well as in finite dimensions, for continuous variables and soft excluded volume constraints, can display entire isostatic phases where local minima of the cost function are marginally stable configurations endowed with non-linear excitations [1,2]. In this work we describe an athermal adiabatic algorithm to explore with continuity the corresponding rough high-dimensional landscape. We concentrate on a prototype problem of this kind, the spherical perceptron optimization problem with linear cost function (hinge loss). This algorithm allows to "surf" between isostatic marginally stable configurations and to investigate some properties of such landscape. In particular we focus on the statistics of avalanches occurring when local minima are destabilized. We show that when perturbing such minima, the system undergoes plastic rearrangements whose size is power law distributed and we characterize the corresponding critical exponent. Finally we investigate the critical properties of the unjamming transition, showing that the linear interaction potential gives rise to logarithmic behavior in the scaling of energy and pressure as a function of the distance from the unjamming point. For some quantities, the logarithmic corrections can be gauged out. This is the case of the number of soft constraints that are violated as a function of the distance from jamming which follows a non-trivial power law behavior.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. IPHT - Institut de Physique Théorique - UMR CNRS 3681

## Survival probability of a run-and-tumble particle in the presence of a drift – Archive ouverte HAL

### Benjamin de Bruyne

^{1}Satya N. Majumdar^{1}Gregory Schehr^{1}#### Benjamin de Bruyne, Satya N. Majumdar, Gregory Schehr. Survival probability of a run-and-tumble particle in the presence of a drift.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2021. ⟨hal-03223973⟩We consider a one-dimensional run-and-tumble particle, or persistent random walk, in the presence of an absorbing boundary located at the origin. After each tumbling event, which occurs at a constant rate $\gamma$, the (new) velocity of the particle is drawn randomly from a distribution $W(v)$. We study the survival probability $S(x,t)$ of a particle starting from $x \geq 0$ up to time $t$ and obtain an explicit expression for its double Laplace transform (with respect to both $x$ and $t$) for an arbitrary velocity distribution $W(v)$, not necessarily symmetric. This result is obtained as a consequence of Spitzer's formula, which is well known in the theory of random walks and can be viewed as a generalization of the Sparre Andersen theorem. We then apply this general result to the specific case of a two-state particle with velocity $\pm v_0$, the so-called persistent random walk (PRW), and in the presence of a constant drift $\mu$ and obtain an explicit expression for $S(x,t)$, for which we present more detailed results. Depending on the drift $\mu$, we find a rich variety of behaviours for $S(x,t)$, leading to three distinct cases: (i) subcritical drift $-v_0\!<\!\mu\!<\! v_0$, (ii) supercritical drift $\mu < -v_0$ and (iii) critical drift $\mu=-v_0$. In these three cases, we obtain exact analytical expressions for the survival probability $S(x,t)$ and establish connections with existing formulae in the mathematics literature. Finally, we discuss some applications of these results to record statistics and to the statistics of last-passage times.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Symmetry Violation of Quantum Multifractality: Gaussian fluctuations versus Algebraic Localization – Archive ouverte HAL

### A. Bilen

^{1}Bertrand Georgeot^{2}O. Giraud^{3}Gabriel Lemarié^{2, 4, 5}I. García-Mata^{1}#### A. Bilen, Bertrand Georgeot, O. Giraud, Gabriel Lemarié, I. García-Mata. Symmetry Violation of Quantum Multifractality: Gaussian fluctuations versus Algebraic Localization.

*Physical Review Research*, American Physical Society, 2021, 3, pp.L022023. ⟨hal-03160414⟩Quantum multifractality is a fundamental property of systems such as non-interacting disordered systems at an Anderson transition and many-body systems in Hilbert space. Here we discuss the origin of the presence or absence of a fundamental symmetry related to this property. The anomalous multifractal dimension $\Delta_q$ is used to characterize the structure of quantum states in such systems. Although the multifractal symmetry relation \mbox{$\Delta_q=\Delta_{1-q}$} is universally fulfilled in many known systems, recently some important examples have emerged where it does not hold. We show that the reason for this is the presence of atypically small eigenfunction amplitudes induced by two different mechanisms. The first one was already known and is related to Gaussian fluctuations well described by random matrix theory. The second one, not previously explored, is related to the presence of an algebraically localized envelope. While the effect of Gaussian fluctuations can be removed by coarse graining, the second mechanism is robust to such a procedure. We illustrate the violation of the symmetry due to algebraic localization on two systems of very different nature, a 1D Floquet critical system and a model corresponding to Anderson localization on random graphs.

- 1. IFIMAR - Instituto de Investigaciones Físicas de Mar del Plata
- 2. LPT - Laboratoire de Physique Théorique
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. UMI 3654 - MajuLab
- 5. CQT - Centre for Quantum Technologies [Singapore]

## The Folded Spin-1/2 XXZ Model: II. Thermodynamics and Hydrodynamics with a Minimal Set of Charges – Archive ouverte HAL

### Lenart Zadnik

^{1}Kemal Bidzhiev^{1}Maurizio Fagotti^{1}#### Lenart Zadnik, Kemal Bidzhiev, Maurizio Fagotti. The Folded Spin-1/2 XXZ Model: II. Thermodynamics and Hydrodynamics with a Minimal Set of Charges.

*SciPost Phys.*, 2021, 10, pp.099. ⟨10.21468/SciPostPhys.10.5.099⟩. ⟨hal-03022690⟩We study the (dual) folded spin-1/2 XXZ model in the thermodynamic limit. We focus, in particular, on a class of local macrostates that includes Gibbs ensembles. We develop a thermodynamic Bethe Ansatz description and work out generalised hydrodynamics at the leading order. Remarkably, in the ballistic scaling limit the junction of two local macrostates results in a discontinuity in the profile of essentially any local observable.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Tracy-Widom Distributions for the Gaussian Orthogonal and Symplectic Ensembles Revisited: A Skew-Orthogonal Polynomials Approach – Archive ouverte HAL

### Anthony Mays

^{1}Anita Ponsaing^{2}Grégory Schehr^{3}#### Anthony Mays, Anita Ponsaing, Grégory Schehr. Tracy-Widom Distributions for the Gaussian Orthogonal and Symplectic Ensembles Revisited: A Skew-Orthogonal Polynomials Approach.

*Journal of Statistical Physics*, Springer Verlag, 2021, 182 (2), ⟨10.1007/s10955-020-02695-w⟩. ⟨hal-03177663⟩We study the distribution of the largest eigenvalue in the "Pfaffian" classical ensembles of random matrix theory, namely in the Gaussian orthogonal (GOE) and Gaussian symplectic (GSE) ensembles, using semi-classical skew-orthogonal polynomials, in analogue to the approach of Nadal and Majumdar (NM) for the Gaussian unitary ensemble (GUE). Generalizing the techniques of Adler, Forrester, Nagao and van Moerbeke, and using "overlapping Pfaffian" identities due to Knuth, we explicitly construct these semi-classical skew-orthogonal polynomials in terms of the semi-classical orthogonal polynomials studied by NM in the case of the GUE. With these polynomials we obtain expressions for the cumulative distribution functions of the largest eigenvalue in the GOE and the GSE. Further, by performing asymptotic analysis of these skew-orthogonal polynomials in the limit of large matrix size, we obtain an alternative derivation of the Tracy-Widom distributions for GOE and GSE. This asymptotic analysis relies on a certain Pfaffian identity, the proof of which employs the characterization of Pfaffians in terms of perfect matchings and link diagrams.

- 1. University of Melbourne
- 2. University of Adelaide
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Two-fluid coexistence in a spinless fermions chain with pair hopping – Archive ouverte HAL

### Lorenzo Gotta

^{1}Leonardo Mazza^{1}Pascal Simon^{2}Guillaume Roux^{1}#### Lorenzo Gotta, Leonardo Mazza, Pascal Simon, Guillaume Roux. Two-fluid coexistence in a spinless fermions chain with pair hopping.

*Phys.Rev.Lett.*, 2021, 126 (20), pp.206805. ⟨10.1103/PhysRevLett.126.206805⟩. ⟨hal-03115808⟩We show that a simple one-dimensional model of spinless fermions with pair hopping displays a phase in which a Luttinger liquid of paired fermions coexists with a Luttinger liquid of unpaired fermions. Our results are based on extensive numerical density-matrix renormalization-group calculations and are supported by a two-fluid model that captures the essence of the coexistence region.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPS - Laboratoire de Physique des Solides