Nonequilibrium quantum order at infinite temperature: spatiotemporal correlations and their generating functions

TL;DR

This paper demonstrates that spatiotemporal correlators can detect quantum order at infinite temperature in disordered systems, revealing eigenstate order through dynamical potentials in both static and Floquet models.

Contribution

It introduces a method using two-time correlators and dynamical potentials to identify quantum order at infinite temperature, overcoming challenges of eigenstate variability.

Findings

Two-time correlators reveal eigenstate order at infinite temperature.

Dynamical potentials exhibit features like bimodal distributions in symmetry-broken phases.

Method applies to static and Floquet spin glass models.

Abstract

Localisation-protected quantum order extends the idea of symmetry breaking and order in ground states to individual eigenstates at arbitrary energy. Examples include many-body localised static and $\pi$-spin glasses in Floquet systems. Such order is inherently dynamical and difficult to detect as the order parameter typically varies randomly between different eigenstates, requiring specific superpositions of eigenstates to be targeted by the initial state. We show that two-time correlators overcome this, reflecting the presence or absence of eigenstate order even in fully-mixed, $infinite$ $temperature$ states. We show how spatiotemporal correlators are generated by the recently introduced dynamical potentials, demonstrating this explicitly using an Ising and a Floquet $\pi$-spin glass and focusing on features mirroring those of equilibrium statistical mechanics such as bimodal potentials in the symmetry-broken phase.