Charges and currents in quantum spin chains: late-time dynamics and spontaneous currents

TL;DR

This paper reviews conservation laws and currents in quantum spin chains, examines how localized defects induce spontaneous currents and disrupt stationary states, and provides numerical evidence that such defects do not lead to thermalization.

Contribution

It offers a formal expression for currents in noninteracting spin chains, analyzes the impact of localized defects on late-time dynamics, and shows that simple defects do not cause thermalization.

Findings

Spontaneous currents emerge near localized defects.

Diagonal ensemble fails to describe late-time dynamics with defects.

Simple localized defects do not induce thermalization.

Abstract

We review the structure of the conservation laws in noninteracting spin chains and unveil a formal expression for the corresponding currents. We briefly discuss how interactions affect the picture. In the second part, we explore the effects of a localized defect. We show that the emergence of spontaneous currents near the defect undermines any description of the late-time dynamics by means of a stationary state in a finite chain. In particular, the diagonal ensemble does not work. Finally, we provide numerical evidence that simple generic localized defects are not sufficient to induce thermalization.