Localization and topology protected quantum coherence at the edge of 'hot' matter

TL;DR

This paper demonstrates that disorder-induced localization in a one-dimensional topological magnet preserves quantum coherence at the edges even at high temperatures, with edge spins exhibiting exponentially long revival times.

Contribution

It shows that disorder can protect quantum coherence at the edges of a topological phase in a highly excited state, a novel insight into hot matter topological protection.

Findings

Edge spins exhibit coherent revival over exponentially long times.

Disorder localizes the system, maintaining topological edge states at high energy.

Quantum coherence persists despite high temperature and disorder.

Abstract

Topological phases are often characterized by special edge states confined near the boundaries by an energy gap in the bulk. On raising temperature, these edge states are lost in a clean system due to mobile thermal excitations. Recently however, it has been established that disorder can localize an isolated many body system, potentially allowing for a sharply defined topological phase even in a highly excited state. Here we show this to be the case for the topological phase of a one dimensional magnet with quenched disorder, which features spin one-half excitations at the edges. The time evolution of a simple, highly excited, initial state is used to reveal quantum coherent edge spins. In particular, we demonstrate, using theoretical arguments and numerical simulation, the coherent revival of an edge spin over a time scale that grows exponentially bigger with system size. This is in sharp contrast to the general expectation that quantum bits strongly coupled to a 'hot' many body system will rapidly lose coherence.