Dynamics at the Many-Body Localization Transition

TL;DR

This paper investigates the dynamical behavior of a one-dimensional Heisenberg model with disorder, revealing two distinct decay regimes in the survival probability linked to localization properties.

Contribution

It provides a detailed analysis of the survival probability dynamics at the many-body localization transition, highlighting the connection to eigenstate multifractality.

Findings

Fast initial decay similar to clean systems

Slower power-law decay at longer times

Decay exponent matches eigenstate multifractal dimension

Abstract

The isolated one-dimensional Heisenberg model with static random magnetic fields has become paradigmatic for the analysis of many-body localization. Here, we study the dynamics of this system initially prepared in a highly-excited nonstationary state. Our focus is on the probability for finding the initial state later in time, the so-called survival probability. Two distinct behaviors are identified before equilibration. At short times, the decay is very fast and equivalent to that of clean systems. It subsequently slows down and develops a powerlaw behavior with an exponent that coincides with the multifractal dimension of the eigenstates.