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

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.

9 pages, 5 figures

References in corpus (14)

• Many body localization and thermalization in quantum statistical mechanics
• Localization of interacting fermions at high temperature
• Many-body localization edge in the random-field Heisenberg chain
• Many body localization in Heisenberg XXZ magnet in a random field
• Equilibrium states of generic quantum systems subject to periodic driving
• Many-body localization in periodically driven systems
• Recent progress in many-body localization
• Absence of diffusion in an interacting system of spinless fermions on a one-dimensional disordered lattice
• Periodically driven ergodic and many-body localized quantum systems
• Observation of Discrete-Time-Crystal Signatures in an Ordered Dipolar Many-Body System
• Interaction dependent heating and atom loss in a periodically driven optical lattice
• Many-body localization, symmetry, and topology
• Methods for calculating nonconcave entropies
• Dynamical potentials for non-equilibrium quantum many-body phases

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• Effective response theory for Floquet topological systems
• Anatomy of localisation protected quantum order on Hilbert space