Extended slow dynamical regime close to the many-body localization transition

TLDR

Many‑body localization is marked by a slow logarithmic increase of entanglement entropy after a global quench while local memory of an initial density imbalance persists indefinitely. This study examines how proximity to a many‑body localized phase affects dynamics in the delocalized, ergodic regime where thermalization is expected. The authors employ an exact Krylov‑space method to simulate the out‑of‑equilibrium dynamics of a random‑field Heisenberg chain up to 28 sites, starting from an initially unentangled high‑energy product state. They find that, throughout most of the delocalized phase, entanglement grows sub‑ballistically as \(S(t)\propto t^{1/z}\) with a disorder‑dependent exponent \(z\ge1\) (in contrast to the ballistic \(z=1\) of clean systems) and that spin imbalance relaxes anomalously as \(\mathcal{I}(t)\propto t^{-\zeta}\) with a disorder‑dependent \(\zeta\) that vanishes at the transition, offering a clear experimental signature of this unconventional regime.

Abstract

Many-body localization is characterized by a slow logarithmic growth of the entanglement entropy after a global quantum quench while the local memory of an initial density imbalance remains at infinite time. We investigate how much the proximity of a many-body localized phase can influence the dynamics in the delocalized ergodic regime where thermalization is expected. Using an exact Krylov space technique, the out-of-equilibrium dynamics of the random-field Heisenberg chain is studied up to $L=28$ sites, starting from an initially unentangled high-energy product state. Within most of the delocalized phase, we find a sub-ballistic entanglement growth $S(t)\ensuremath{\propto}{t}^{1/z}$ with a disorder-dependent exponent $z\ensuremath{\ge}1$, in contrast with the pure ballistic growth $z=1$ of clean systems. At the same time, anomalous relaxation is also observed for the spin imbalance $\mathcal{I}(t)\ensuremath{\propto}{t}^{\ensuremath{-}\ensuremath{\zeta}}$ with a continuously varying disorder-dependent exponent $\ensuremath{\zeta}$, vanishing at the transition. This provides a clear experimental signature for detecting this nonconventional regime.