Thibault Scoquart (LPT Toulouse/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)