Entanglement Dynamics of Disordered Quantum XY Chains

TL;DR

This paper investigates how disorder affects entanglement and particle transport in quantum XY chains, demonstrating bounded entanglement over time and localized particle dynamics under Anderson localization assumptions.

Contribution

It establishes that disorder leads to bounded entanglement and localized particle transport in quantum XY chains, extending understanding of many-body localization effects.

Findings

Entanglement remains bounded for all times in disordered XY chains.

Particle transport is significantly suppressed, with dynamics confined near initial interval edges.

Results hold under assumptions typical of Anderson localization in the associated one-particle Hamiltonian.

Abstract

We consider the dynamics of the quantum XY chain with disorder under the general assumption that the expectation of the eigenfunction correlator of the associated one-particle Hamiltonian satisfies a decay estimate typical of Anderson localization. We show that, starting from a broad class of product initial states, entanglement remains bounded for all times. For the XX chain, we also derive bounds on the particle transport which, in particular, show that the density profile of initial states that consist of fully occupied and empty intervals, only have significant dynamics near the edges of those intervals, uniformly for all times.