Nonequilibrium many-body steady states via Keldysh formalism

TL;DR

This paper uses the Keldysh formalism to analyze nonequilibrium steady states in many-body systems, revealing limitations of mean field theory and uncovering universal thermodynamic behavior due to dissipation.

Contribution

It systematically investigates the validity of mean field theory in non-equilibrium many-body states using a field-theoretic approach based on the Keldysh formalism.

Findings

Mean field theory often fails to accurately describe non-equilibrium steady states.

An effective temperature emerges from dissipation in these systems.

Universal behavior near steady states aligns with thermodynamic universality classes.

Abstract

Many-body systems with both coherent dynamics and dissipation constitute a rich class of models which are nevertheless much less explored than their dissipationless counterparts. The advent of numerous experimental platforms that simulate such dynamics poses an immediate challenge to systematically understand and classify these models. In particular, nontrivial many-body states emerge as steady states under non-equilibrium dynamics. While these states and their phase transitions have been studied extensively with mean field theory, the validity of the mean field approximation has not been systematically investigated. In this paper, we employ a field-theoretic approach based on the Keldysh formalism to study nonequilibrium phases and phase transitions in a variety of models. In all cases, a complete description via the Keldysh formalism indicates a partial or complete failure of the mean field analysis. Furthermore, we find that an effective temperature emerges as a result of dissipation, and the universal behavior including the dynamics near the steady state is generically described by a thermodynamic universality class.