From Anderson to Many-Body Localization: Instabilities in the Random-Field XXZ Chain

by Jeanne Colbois (Institut Néel Grenoble)

Thursday Jul 31, 2025, 2:15 PM → 3:45 PM Europe/Berlin

D6-135 (UHG)

Isolated many-body quantum interacting systems in the presence of disorder are notoriously difficult to study, yet they raise fundamental questions in quantum statistical physics.  In 1958, Anderson formulated a simple problem. For a fermion jumping in a random potential, he showed that, for strong enough disorder, all eigenstates  - even at high energy - are localized. This  provides an example of a "real system with an infinite number of degrees of freedom (...) in which the approach to equilibrium is simply impossible" [1]. How do interactions modify this picture ? Can localization persist at finite energy density, giving rise to a genuinely non-ergodic many-body phase ? 

Despite nearly two decades of intense study [2], the existence and stability of such a many-body localized (MBL) phase remains debated [3], even one dimension where localization is expected to be most robust.  In this talk, I introduce the key notions behind MBL and provide a selective overview of the ongoing debate, focusing to a large extent on the eigenstate properties of a paradigmatic model: the random-field spin-1/2 Heisenberg chain. Within this context, I will present results from our recent comprehensive shift-invert exact diagonalization studies and discuss their possible implications for instabilities - or the absence thereof - of the many-body localized regime.

[1] Anderson, Phys. Rev. 1958
[2] Basko, Aleiner, Altschuler, Annals of Physics,  2006
[3] Sierant, Lewenstein, Scardicchio, Vidmar, Zakrewski, Rep. Prog. Phys, 2025

2025-07-31_Colbois_Jeanne.pdf