Absence of localization in interacting spin chains with a discrete symmetry

TL;DR

This paper proves that certain symmetric spin chains exhibit finite spin transport at high temperature and zero magnetization, demonstrating delocalization mechanisms that are robust to symmetry breaking.

Contribution

It provides a rigorous proof of delocalization in symmetric spin chains and demonstrates the robustness of this phenomenon through numerical examples.

Findings

Spin chains with specific symmetries show finite spin transport.

Delocalization persists across energy densities and symmetry breaking.

Coupled localized systems can induce delocalization in each other.

Abstract

We prove that spin chains symmetric under a combination of mirror and spin-flip symmetries and with a nondegenerate spectrum show finite spin transport at zero total magnetization and infinite temperature. We demonstrate this numerically using two prominent examples: the Stark many-body localization system and the symmetrized many-body localization system. We provide evidence of delocalization at all energy densities and show that the delocalization mechanism is robust to breaking the symmetry. We use our results to construct two localized systems which, when coupled, delocalize each other.