Dynamical potentials for non-equilibrium quantum many-body phases

TL;DR

This paper introduces dynamical potentials as generating functions for spatiotemporal correlations, enabling characterization of non-equilibrium quantum many-body phases like many-body localization and time crystals.

Contribution

It presents a novel framework of dynamical potentials that generalize thermodynamic potentials to non-equilibrium quantum phases, demonstrated through three key examples.

Findings

Dynamical potentials effectively characterize eigenstate phases.

Application to disordered XXZ chain reveals many-body localization.

Application to disordered Ising chain shows spin-glass and time-crystalline order.

Abstract

Out of equilibrium phases of matter exhibiting order in individual eigenstates, such as many-body localised spin glasses and discrete time crystals, can be characterised by inherently dynamical quantities such as spatiotemporal correlation functions. In this work, we introduce dynamical potentials which act as generating functions for such correlations and capture eigenstate phases and order. These potentials show formal similarities to their equilibrium counterparts, namely thermodynamic potentials. We provide three representative examples: a disordered, many-body localised XXZ chain showing many-body localisation, a disordered Ising chain exhibiting spin-glass order and its periodically-driven cousin exhibiting time-crystalline order.