Exact strong zero modes in quantum circuits and spin chains with non-diagonal boundary conditions

TL;DR

This paper constructs exact strong zero mode operators in integrable quantum circuits and spin chains with non-diagonal boundary conditions, revealing their boundary localization and implications for boundary coherence.

Contribution

It introduces a method to construct exact strong zero modes in systems with open boundaries, extending understanding of boundary effects in quantum integrable models.

Findings

ESZM are localized around boundaries

ESZM induce infinite boundary coherence times

ESZM become non-local under the ASEP mapping

Abstract

We construct exact strong zero mode operators (ESZM) in integrable quantum circuits and the spin-1/2 XXZ chain for general open boundary conditions, which break the bulk U(1) symmetry of the time evolution operators. We show that the ESZM is localized around one of the boundaries and induces infinite boundary coherence times. Finally, we prove that the ESZM becomes spatially non-local under the map that relates the spin-1/2 XXZ chain to the asymmetric simple exclusion process, which suggests that it does not play a significant role in the dynamics of the latter.