Tracking locality in time evolution of disordered systems

TL;DR

This paper introduces a correlation function difference (CFD) to analyze information transfer in disordered quantum spin systems, revealing distinct dynamical behaviors in ergodic and localized regimes.

Contribution

The paper proposes a new CFD measure to study locality and information propagation in disordered quantum systems, providing insights into different dynamical phases.

Findings

CFD propagates faster than spin transport in ergodic phase

CFD relaxes exponentially slowly in localized phases

CFD offers a new perspective on non-local correlations

Abstract

Using local density correlation functions for a one-dimensional spin system, we introduce a correlation function difference (CFD) which compares correlations on a given site between a full system of size $L$ and its restriction to $\ell<L$ sites. We show that CFD provides useful information on transfer of information in quantum many-body systems by considering the examples of ergodic, Anderson, and many-body localized regimes in disordered XXZ spin chain. In the ergodic phase, we find that the propagation of CFD is asymptotically faster than the spin transport but slower than the ballistic propagation implied by the Lieb-Robinson bound. In contrast, in the localized cases, we unravel an exponentially slow relaxation of CFD. Connections between CFD and other observables detecting non-local correlations in the system are discussed.