A Lieb-Robinson bound for quantum spin chains with strong on-site impurities

TL;DR

This paper establishes a Lieb-Robinson bound for quantum spin chains with sparse, strong on-site impurities, providing new insights into the dynamics and information propagation in disordered quantum systems.

Contribution

It introduces a novel Lieb-Robinson bound that accounts for impurity coupling strengths and applies to both finite and infinite systems, advancing understanding of disordered quantum spin chains.

Findings

Derived commutator bounds incorporating impurity strengths

Improved Lieb-Robinson bounds for chains with heavy-tailed disorder

Applicable to both finite volume and thermodynamic limit

Abstract

We consider a quantum spin chain with nearest neighbor interactions and sparsely distributed on-site impurities. We prove commutator bounds for its Heisenberg dynamics which incorporate the coupling strengths of the impurities. The impurities are assumed to satisfy a minimum spacing, and each impurity has a non-degenerate spectrum. Our results are proven in a broadly applicable setting, both in finite volume and in thermodynamic limit. We apply our results to improve Lieb-Robinson bounds for the Heisenberg spin chain with a random, sparse transverse field drawn from a heavy-tailed distribution.