Logarithmic current fluctuations in non-equilibrium quantum spin chains

TL;DR

This paper investigates current fluctuations in non-equilibrium quantum spin chains, revealing a logarithmic growth in variance and extending findings from the XX model to the XXZ model in the critical region.

Contribution

It derives an exact variance expression for the XX model and argues the logarithmic growth applies to the XXZ model in the critical phase.

Findings

Variance of spin current grows logarithmically over time

Exact expression for variance in the XX model

Logarithmic growth likely extends to the XXZ model

Abstract

We study zero-temperature quantum spin chains which are characterized by a non-vanishing current. For the XX model starting from the initial state |... + + + - - - ...> we derive an exact expression for the variance of the total spin current. We show that asymptotically the variance exhibits an anomalously slow logarithmic growth; we also extract the sub-leading constant term. We then argue that the logarithmic growth remains valid for the XXZ model in the critical region.