Edge bits in average symmetry protected topological mixed state

TL;DR

This paper investigates edge bits in average symmetry protected topological mixed states, revealing their robustness and fractionalization properties under certain symmetries, with numerical analysis confirming persistent edge correlations.

Contribution

It introduces a framework for understanding edge bits in ASPT mixed states protected by $Z_2$ symmetries, highlighting their fractionalization and robustness through numerical and operator-space mutual information analysis.

Findings

Edge bits exhibit symmetry fractionalization similar to pure SPT states.

Edge-to-edge correlations partially survive decoherence and perturbations.

Numerical results confirm the robustness of edge bits in ASPT states.

Abstract

Edge bit in an average symmetry protected topological (ASPT) mixed state is studied. The state is protected by one strong $Z_2$ and one weak (average) $Z_2$ symmetries. As analogous objects of pure symmetry protected topological (SPT) states, the ASPT possesses edge bits. In particular, the analogous operator response exists, that is, symmetry fractionalization. The fractionalization preserves the presence of the ASPT in the bulk, and the fractionalized edge operators acting on the edge bits of the ASPT. %analogous to the ones in the pure SPTs. In this work, based on the cluster model and by employing Choi mapping, we discuss generic features of the edge bits and numerically clarify the behavior of the edge bits and their robustness for varying decoherence and perturbative interactions. By using an operator-space mutual information (OSMI), we track the flow of quantum correlations between the two edges. Remarkably, even in the ASPT regime, a finite portion of the initial edge-to-edge correlation survives.