# Séminaires du mardi 27 février

## Séminaire du LPTMS: Andrea de Luca

#### 11:00:00

## Solution of a minimal model for many-body quantum chaos

### Andrea de Luca (Rudolf Peierls Centre for Theoretical Physics, Oxford University, UK)

I present a minimal model for quantum chaos in a spatially extended many-body system. It consists of a chain of sites with nearest-neighbour coupling under Floquet time evolution. Quantum states at each site span a q-dimensional Hilbert space and time evolution for a pair of sites is generated by a q^{2}×q

^{2}random unitary matrix. The Floquet operator is specified by a quantum circuit, in which each site is coupled to its neighbour on one side during the first half of the evolution period, and to its neighbour on the other side during the second half of the period. I will introduce a diagrammatic formalism useful to average the many-body dynamics over realisations of the random matrices. This approach leads to exact expressions in the large-q limit and sheds light on the universality of random matrices in many-body quantum systems and the ubiquitous entanglement growth in out-of-equilibrium dynamics.

## Séminaire du LPTMS: Laurent de Forges de Parny

#### 11:30:00

## Multicomponent Bose-Hubbard Model: Nematic Order in Spinor Condensates

### Laurent de Forges de Parny (Albert-Ludwigs University of Freiburg, Germany)

Since the seminal work of D. Jaksch et al. [1], the motivation of considering bosonic mixtures has emerged from the promising perspectives of observing coexisting quantum phases, spin-dynamics, and quantum magnetism. Recently, ultracold bosons with effective spin degree of freedom allowed to engineer magnetic quantum phase transitions and non trivial magnetic phases, e.g. the nematic order, which breaks the spin-rotation symmetry without magnetic order [2]. I will discuss the magnetic properties of strongly interacting spin-1 bosons in optical lattices. Employing a combined strategy based on exact numerical methods (quantum Monte Carlo simulations and exact diagonalization) and analytical calculations, we have derived the phase diagrams and characterized the phase transitions beyond the mean field description [3,4]. Furthermore, we have established the low energy spectrum of the nematic superfluid phase and have confirmed a singlet-to-nematic phase transition inside the Mott insulator phase. References:- D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner and P. Zoller,
*Cold Bosonic Atoms in Optical Lattices*, Phys. Rev. Lett.**81**, 3108 (1998) - T. Zibold, V. Corre, C. Frapolli, A. Invernizzi, J. Dalibard and F. Gerbier, Spin-nematic order in antiferromagnetic spinor condensates, Phys. Rev. A
**93**, 023614 (2016). - L. de Forges de Parny, F. Hébert, V. G. Rousseau, and G. G. Batrouni, Interacting spin-1 bosons in a two-dimensional optical lattice, Phys. Rev. B
**88**, 104509 (2013). - Laurent de Forges de Parny, Hongyu Yang, and Frédéric Mila,
*Anderson Tower of States and Nematic Order of Spin-1 Bosonic Atoms on a 2D Lattice*, Phys.Rev.Lett.**113**, 200402 (2014)