# 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

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

### Tristan Gautié

^{1}Naftali R. Smith^{1, 2}#### 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. LPENS (UMR_8023) - Laboratoire de physique de l'ENS - ENS Paris
- 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. LPENS (UMR_8023) - Laboratoire de physique de l'ENS - ENS Paris
- 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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. LPENS (UMR_8023) - Laboratoire de physique de l'ENS - ENS Paris
- 2. 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