Local integrals of motion detection of localization-protected topological order

TL;DR

This paper introduces a method using local integrals of motion parametrized by quantum circuits to distinguish topologically distinct many-body localized phases, demonstrated on a fermionic chain and extendable to higher dimensions.

Contribution

It presents a novel approach to identify topological order in MBL phases through variational local integrals of motion, surpassing traditional order parameters.

Findings

Successfully distinguished topologically different MBL phases in a fermionic chain.

Extracted high-energy topological doublets using the DMRG-X algorithm.

Proposed extension of methods to higher-dimensional systems for hidden topological order.

Abstract

Many-body-localized (MBL) phases can be topologically distinct, but distinguishing these phases using order parameters can be challenging. Here we show how topologically distinct local integrals of motion, variationally parametrized by quantum circuits, can be used to numerically demonstrate the topological inequivalence of MBL phases. We illustrate our approach on a fermionic chain where both topologically distinct MBL phases and benchmark comparisons to order parameters are possible. We also use our approach, augmented by the DMRG-X algorithm, to extract high-energy topological doublets. We describe applying our methods to higher dimensions to identify MBL topological order and topological multiplets hidden by the dense many-body spectrum.