Accessing eigenstate spin-glass order from reduced density matrices

TL;DR

This paper introduces a new method to detect many-body localized spin-glass order using two-site reduced density matrices, enabling experimental observation in current quantum systems.

Contribution

It presents an eigenstate spin-glass order parameter derived from reduced density matrices, facilitating detection of MBL-SG phases in experiments.

Findings

Eigenstate spin-glass order parameter effectively detects MBL-SG phases.

Method applicable to both eigenstates and nonequilibrium dynamics.

Potential for experimental observation in Rydberg and trapped ion systems.

Abstract

Many-body localized phases may not only be characterized by their ergodicity breaking, but can also host ordered phases such as the many-body localized spin-glass (MBL-SG). The MBL-SG is challenging to access in a dynamical measurement and therefore experimentally since the conventionally used Edwards-Anderson order parameter is a two-point correlation function in time. In this work, we show that many-body localized spin-glass order can also be detected from two-site reduced density matrices, which we use to construct an eigenstate spin-glass order parameter. We find that this eigenstate spin-glass order parameter captures spin-glass phases in random Ising chains both in many-body eigenstates as well as in the nonequilibrium dynamics from a local in time measurement. We discuss how our results can be used to observe MBL-SG order within current experiments in Rydberg atoms and trapped ion systems.