Probability transport on the Fock space of a disordered quantum spin chain

TL;DR

This paper studies how probability distributions evolve over time on the Fock space of a disordered quantum spin chain, revealing distinct behaviors in ergodic and many-body localized phases, with implications for understanding quantum dynamics.

Contribution

It provides a detailed quantitative analysis of probability transport and dynamics on the Fock space across the many-body localization transition in a disordered quantum spin chain.

Findings

Inhomogeneous dynamics at intermediate times in both phases.

Homogenization of dynamics at long times in the ergodic phase.

Persistent inhomogeneity and multifractality in the localized phase.

Abstract

Within the broad theme of understanding the dynamics of disordered quantum many-body systems, one of the simplest questions one can ask is: given an initial state, how does it evolve in time on the associated Fock-space graph, in terms of the distribution of probabilities thereon? A detailed quantitative description of the temporal evolution of out-of-equilibrium disordered quantum states and probability transport on the Fock space, is our central aim here. We investigate it in the context of a disordered quantum spin chain which hosts a disorder-driven many-body localisation transition. Real-time dynamics/probability transport is shown to exhibit a rich phenomenology, which is markedly different between the ergodic and many-body localised phases. The dynamics is for example found to be strongly inhomogeneous at intermediate times in both phases, but while it gives way to homogeneity at long times in the ergodic phase, the dynamics remain inhomogeneous and multifractal in nature for arbitrarily long times in the localised phase. Similarly, we show that an appropriately defined dynamical lengthscale on the Fock-space graph is directly related to the local spin-autocorrelation, and as such sheds light on the (anomalous) decay of the autocorrelation in the ergodic phase, and lack of it in the localised phase.