Energy transport in a disordered spin chain with broken U(1) symmetry: Diffusion, subdiffusion, and many-body localization

TL;DR

This paper investigates energy transport in a disordered XYZ spin chain, revealing ballistic, diffusive, subdiffusive, and localized regimes, and how anisotropy influences the transition to many-body localization.

Contribution

It provides a detailed numerical analysis of energy transport regimes in the disordered XYZ spin chain, highlighting the impact of anisotropy on localization transition.

Findings

Ballistic transport in clean XYZ chain.

Stable diffusive regime at weak disorder.

Transition to subdiffusion and localization at higher disorder.

Abstract

We explore the physics of the disordered XYZ spin chain using two complementary numerical techniques: exact diagonalization (ED) on chains of up to 17 spins, and time-evolving block decimation (TEBD) on chains of up to 400 spins. Our principal findings are as follows. First, the clean XYZ spin chain shows ballistic energy transport for all parameter values that we investigated. Second, for weak disorder there is a stable diffusive region that persists up to a critical disorder strength that depends on the XY anisotropy. Third, for disorder strengths above this critical value energy transport becomes increasingly subdiffusive. Fourth, the many-body localization transition moves to significantly higher disorder strengths as the XY anisotropy is increased. We discuss these results, and their relation to our current physical picture of subdiffusion in the approach to many-body localization.