Clustering of non-ergodic eigenstates in quantum spin glasses

TL;DR

This paper reveals a non-ergodic eigenstate phase in quantum p-spin models that violates ETH without being MBL, characterized by a mobility edge and clustered eigenstates with distinct magnetization patterns.

Contribution

It identifies a novel non-ergodic phase in quantum spin glasses, located between ergodic and MBL phases, with a detailed characterization of eigenstate clustering and phase boundaries.

Findings

Existence of a non-ergodic eigenstate phase violating ETH

Location of a mobility edge separating phases

Eigenstates form clusters with distinct magnetization patterns

Abstract

The two primary categories for eigenstate phases of matter at finite temperature are many-body localization (MBL) and the eigenstate thermalization hypothesis (ETH). We show that in the paradigmatic quantum $p$-spin models of spin-glass theory, eigenstates violate ETH yet are not MBL either. A mobility edge, which we locate to leading order in $1/p$ using the forward-scattering approximation and replica techniques, separates the non-ergodic phase at small transverse field from an ergodic phase at large transverse field. The non-ergodic phase is also bounded from above in temperature, by a transition in configuration-space statistics reminiscent of the clustering transition in spin-glass theory. We show that the non-ergodic eigenstates are organized in clusters which exhibit distinct magnetization patterns, as characterized by an eigenstate variant of the Edwards-Anderson order parameter.