Many-Body Spectral Reflection Symmetry and Protected Infinite-Temperature Degeneracy

TL;DR

This paper explores a new form of protected degeneracy in many-body quantum systems caused by spectral reflection symmetry, revealing exponentially many zero modes at infinite temperature and proposing experimental detection methods.

Contribution

It introduces the concept of spectral reflection symmetry protecting zero modes at infinite temperature and provides a dynamical protocol for their detection in Rydberg atom experiments.

Findings

Number of zero modes grows exponentially with system size.

Proposed a feasible experimental protocol for detection.

Zero energy states show unique eigenstate properties.

Abstract

Protected zero modes in quantum physics traditionally arise in the context of ground states of many-body Hamiltonians. Here we study the case where zero modes exist in the center of a reflection-symmetric many-body spectrum, giving rise to the notion of a protected "infinite-temperature" degeneracy. For a certain class of nonintegrable spin chains, we show that the number of zero modes is determined by a chiral index that grows exponentially with system size. We propose a dynamical protocol, feasible in ongoing experiments in Rydberg atom quantum simulators, to detect these many-body zero modes and their protecting spectral reflection symmetry. Finally, we consider whether the zero energy states obey the eigenstate thermalization hypothesis, as is expected of states in the middle of the many-body spectrum. We find intriguing differences in their eigenstate properties relative to those of nearby nonzero-energy eigenstates at finite system sizes.