Dynamics of non-equilibrium steady state quantum phase transitions

TL;DR

This paper extends the Kibble-Zurek mechanism to driven-dissipative quantum systems, demonstrating universal scaling in non-equilibrium steady states and clarifying adiabaticity and excitations in open quantum systems.

Contribution

It generalizes the Kibble-Zurek mechanism to open quantum systems and introduces a method to characterize non-adiabatic excitations using instantaneous steady states.

Findings

Universal Kibble-Zurek scaling observed in open transverse Ising model

Applicability demonstrated in an open Landau-Zener problem

Clarification of adiabaticity and excitations in driven-dissipative systems

Abstract

In this paper we address the question how the Kibble-Zurek mechanism, which describes the formation of topological defects in quantum systems subjected to a quench across a critical point, is generalized to the same scenario but for driven-dissipative quantum critical systems. In these out of equilibrium systems, the critical behavior is manifested in the steady states rather than in the ground states as in quantum critical models of closed systems. To give the generalization we need to establish what is meant by adiabaticity in open quantum systems. Another most crucial concept that we clarify is the characterization of non-adiabatic excitations. It is clear what these are for a Hamiltonian systems, but question is more subtle for driven-dissipative systems. In particular, the important observation is that the instantaneous steady states serve as reference states. From these the excitations can then be extracted by comparing the distance from the evolved state to the instantaneous steady state. With these issues resolved we demonstrate the applicability of the generalized Kibble-Zurek mechanism to an open Landau-Zener problem and show universal Kibble-Zurek scaling for an open transverse Ising model. Thus, our results support any assumption that non-equilibrium quantum critical behavior can be understood from universal features.