Séminaires du LPTMC

Salle 523, couloir 12-13, 5è étage

Scaling of many-body localization transitions: Correlations and dynamics in Fock space and real space

Many-body localization (MBL) is a remarkable phenomenon where interacting quantum systems fail to thermalize due to disorder. Despite two decades of intense theoretical and numerical work, there is still no clear consensus on whether a true 1D MBL phase exists in the thermodynamic limit, or whether it eventually gives way to slow thermalization.

After a broad introduction to the current open questions surrounding MBL, I will discuss recent results [1] on how MBL transitions scale with system size in several different disordered spin-½ models. By representing these models as effective tight-binding problems in Fock space—where “sites’’ correspond to many-body basis states and “hoppings’’ to interactions—we can explicitly identify the role of correlations between Fock-space energies and couplings in the onset of localization and the breakdown of ergodicity. Comparing models with and without such correlations (1D spin chains, quantum dot with all-to-all interactions, and the quantum random energy model) reveals strikingly different scaling behaviors for the critical disorder strength and transition width, which we predicted analytically and verified numerically. Finally, I will show how real-space dynamical probes that are accessible to modern simulators, such as the time evolution of the “generalized” imbalance, also capture the features of the transition from the Fock-space perspective, and allow us to construct consistent finite-size phase diagrams, in full agreement with spectral observables [2].

[1] T. Scoquart, I. Gornyi and A. Mirlin, Role of Fock-space correlations in many-body localization, Phys. Rev. B 109, 214203, (2024)
[2] T. Scoquart, I. Gornyi and A. Mirlin, Scaling of many-body localization transitions: Quantum dynamics in Fock space and real space, Phys. Rev. B 112, 064203 (2025)

Salle 523, couloir 12-13, 5è étage

The "Mode-Shell" correspondence, a unifying concept in topological physics

In quantum or classical wave systems, some properties of wave systems are known to be topologically protected. Due to their increased robustness, such properties have attracted much interest in the past decades.

The most studied case is the existence of unidirectional edge states in the quantum Hall effect and, more generally, the existence of protected states at the edges of topologically insulators. An important result is then the bulk-edge correspondence that links the existence of topological edge states to a topological index defined in the volume of the material.

This is not the only case studied in topological physics and different, yet similar, results have been obtained for topological semimetals, higher order insulators or continuous wave systems. In this talk I will explain how all these results can be understood in a unifying theory using the mode-shell correspondence formalism which relates the existence of isolated topological modes in phase space, to a topological invariant defined in the surface which encloses these modes in phase space. Invariant that reduces to Chern or winding numbers in the semiclassical limit.

Mode-shell correspondence, a unifying phase space theory in topological physics
[1] Part I: Chiral number of zero-modes https://www.scipost.org/10.21468/SciPostPhys.17.2.060
[2] Part II: Higher-dimensional spectral invariants https://arxiv.org/abs/2501.13550

Salle 523, couloir 12-13, 5è étage

Excitations in triangular-lattice antiferromagnets near the Ising limit

Recent experimental studies have stimulated an extensive interest on the excitation spectrum of spin-1/2 triangular magnets with XXZ magnetic anisotropy. Among the materials which were recently investigated, the cobaltite K2Co(SeO3)2 was demonstrated to realize an XXZ triangular magnet with an extremely strong degree of easy-axis anisotropy, implying that the compound is located very close to the limit of a quantum Ising model with transverse exchange. Motivated by the inelastic neutron scattering studies on this compound, this presentation will report on a theoretical analysis of the excitation spectrum in the "up-up-down" and in the low-field phase of the model, focusing on the Ising limit in which the longitudinal exchange Jzz is much larger than the transverse exchange Jxy. In the “up-up-down” phase, stabilized by a c-axis oriented field, we study the magnon excitations, both in the framework of spin wave theory and within a perturbative expansion in the anisotropy parameter α = Jxy/Jzz ≪ 1. We show that the linear-spin wave (LSW) approximation, although exact at leading order in α, severely underestimates the coefficients of the higher-order corrections in α. It will be shown that this discrepancy explains the deviations between LSW and scattering data observed in the up-up-down phase. The presentation will then discuss the spectrum in the case of zero field, for which the system is characterized by "spin-supersolid" long-range order. We analyze the first-order non-linear spin wave corrections to the linear spin wave theory, and show that the 1/S nonlinearities do not provide a simple framework for explaining the anomalous spectral features observed experimentally in K2Co(SeO3)2.

Salle 523, couloir 12-13, 5è étage

Hybrid between biologically inspired and quantum inspired many-body states

Deep neural networks can represent very different sorts of functions, including complex quantum many-body states. Tensor networks can also represent these states, have more structure and are easier to optimize. However, they can be prohibitively costly computationally in two or higher dimensions. In this seminar I will propose a hybrid network [1] which borrows features from the two different formalisms. I will showcase the ansatz by obtaining the representation of a transverse field quantum Ising model with a long range 1/r^6 antiferromagnetic interaction on a 10×10 square lattice. The model corresponds to the Rydberg (cold) atoms platform proposed for quantum annealing.

[1] Srdinsek, Waintal, arXiv:2506.05050 (2025)

Salle 523, couloir 12-13, 5è étage

Exceptional Stationary State in a Dephasing Many-Body Open Quantum System

The late-time dynamics of many-body systems is one of the central problems in statistical mechanics. The eventual emergence of Gibbs ensembles at late times for closed systems is usually explained using the Eigenstate Thermalization Hypothesis (ETH): it postulates, among other things, local indistinguishability of the energy eigenstates and proper statistical ensembles. Rare eigenstates that violate ETH are known as many-body scars and can affect the dynamics of the system in a non-trivial way.

We investigate a related mechanism for an open quantum many-body system. In particular, we focus on a model that hosts, together with the infinite-temperature state, another additional stationary state. The latter is exceptional in many respects and plays the role of a quantum scar. We discuss the properties of the model, focusing on the fate of interfaces between the two states. We find that at late times an effective description is based on stochastic fluctuations of the interface; in particular, the scar is progressively eroded at a finite velocity, and the interface broadens diffusively. While this mechanism resembles hydrodynamics of local conserved charges, important differences are pointed out.

This is a joint work with Alice Marché, Gianluca Morettini, Leonardo Mazza, and Lorenzo Gotta [Phys. Rev. Lett. 135, 020406 (2025)]

Salle 523, couloir 12-13, 5è étage

A perturbative approach to the macroscopic fluctuation theory

The typical behavior of a large class of microscopic diffusive dynamics can be described by macroscopic PDEs and the fluctuations are also well encoded by the dynamical large deviations. This macroscopic description is fully determined by 2 transport coefficients, namely the diffusion coefficient and the conductivity. A great achievement of the macroscopic fluctuation theory is to represent the density large deviations of the corresponding stationary states in terms of a macroscopic variational principle (known as the quasi-potential). For general transport coefficients, this dynamical variational principle is not explicit and a closed form has been only obtained for a restricted class of models.

In a small forcing regime, we will explain how the large deviation functional of the density can be computed perturbatively by using the macroscopic fluctuation theory. This applies to general domains in any dimension and to diffusive dynamics with arbitrary transport coefficients. [Joint work with B. Derrida]