Energy diffusion in the ergodic phase of a many body localizable spin chain

TL;DR

This paper investigates energy transport in disordered quantum spin chains, revealing that energy diffusion breaks down before the many-body localization transition, indicating a complex ergodic phase with anomalous transport properties.

Contribution

It uncovers the breakdown of energy diffusion prior to the many-body localization transition and identifies a peculiar ergodic phase with subdiffusive spin transport.

Findings

Energy diffusion breaks down before the MBL transition.

Energy remains diffusive in a region where spin transport is subdiffusive.

Energy transport is slower than spin transport in the ergodic phase.

Abstract

The phenomenon of many-body localization in disordered quantum many-body systems occurs when all transport is suppressed despite the fact that the excitations of the system interact. In this work we report on the numerical simulation of autonomous quantum dynamics for disordered Heisenberg chains when the system is prepared with an initial inhomogeneity in the energy density profile. Using exact diagonalisation and a dynamical code based on Krylov subspaces we are able to simulate dynamics for up to L = 26 spins. We find, surprisingly, the breakdown of energy diffusion even before the many-body localization transition whilst the system is still in the ergodic phase. Moreover, in the ergodic phase we also find a large region in parameter space where the energy dynamics remains diffusive but where spin transport has been previously evidenced to occur only subdiffusively: this is found to be true for initial states composed of infinitely many hydrodynamic modes (square-wave energy profile) or just the single longest mode (sinusoidal profile). This suggestive finding points towards a peculiar ergodic phase where particles are transported slower than energy, reminiscent of the situation in amorphous solids and of the gapped phase of the anisotropic Heisenberg model.