Localisation and Sub-Diffusive Transport in Quantum Spin Chains With Dilute Disorder

TL;DR

This paper investigates how dilute disorder affects many-body localisation in quantum spin chains, revealing conditions under which localisation breaks down and sub-diffusive transport emerges, thus providing insights into Griffiths effects.

Contribution

The study introduces models with controllable dilute disorder to explore the stability and breakdown of localisation in quantum spin chains.

Findings

Localisation remains stable at strong disorder despite high thermal region concentration.

Evidence of slow dynamics and sub-diffusive transport at moderate disorder levels.

Dilute disorder models can effectively study Griffiths effects in disordered systems.

Abstract

It is widely believed that many-body localisation in one dimension is fragile and can be easily destroyed by thermal inclusions, however there are still many open questions regarding the stability of the localised phase and under what conditions it breaks down. Here I construct models with dilute disorder, which interpolate between translationally invariant and fully random models, in order to study the breakdown of localisation. This opens up the possibility to controllably increase the density of thermal regions and examine the breakdown of localisation as this density is increased. At strong disorder, the numerical results are consistent with commonly-used diagnostics for localisation even when the concentration of thermalising regions is high. At moderate disorder, I present evidence for slow dynamics and sub-diffusive transport across a large region of the phase diagram, suggestive of a `bad metal' phase. This suggests that dilute disorder may be a useful effective model for studying Griffiths effects in many-body localisation, and perhaps also in a wider class of disordered systems.