Many-body localization through imbalance statistics: transition scaling and rare resonances
Thibault Scoquart (LPT, Toulouse)
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 explain why the fate of the localized regime is, at its core, controlled by the system’s ability to form resonances across the exponentially large many-body Hilbert space — pairs of configurations close in energy and coupled by interactions. A growing consensus in the literature is that the relevant resonances are rare events, both in real space and in Fock space, which is why disorder-averaged quantities can be misleading: the physics of MBL hides in the fluctuations and distributions of dynamical observables.
I will illustrate this through recent work on the imbalance, a standard dynamical probe of the memory of an initial state in MBL experiments, examined at two complementary levels. Across a family of disordered spin models with different Fock-space correlation structures [1], I will first show how the scaling of the MBL crossover with system size is faithfully tracked by the quantum and mesoscopic fluctuations of a « generalized » imbalance, yielding finite-size phase diagrams and transition widths in agreement with spectral observables [2]. I will then turn to the deep localized regime, where we recently showed that the standard, site-averaged imbalance hides a much richer microscopic structure: the full distribution of site-resolved imbalances exhibits direct fingerprints of rare local resonances between a few neighboring spins, quantitatively captured by a simple analytical toy model [3].
[1] T. Scoquart, I. Gornyi and A. Mirlin, Phys. Rev. B 109, 214203 (2024)
[2] T. Scoquart, I. Gornyi and A. Mirlin, Phys. Rev. B 112, 064203 (2025)
[3] A. Haldar, T. Scoquart, F. Alet and N. Laflorencie, arXiv:2601.05177 (2026)