On a quantum phase transition in a steady state out of equilibrium

TL;DR

This paper demonstrates a quantum phase transition in a nonequilibrium steady state of a quasifree fermionic system, showing translation invariance breaking and positive entropy production, driven by an external magnetic field.

Contribution

It establishes the existence of a second-order quantum phase transition in a nonequilibrium setting within an axiomatic framework for large quantum systems.

Findings

The steady state breaks translation invariance.

The entropy production rate is strictly positive.

A second-order quantum phase transition occurs with magnetic field strength.

Abstract

Within the rigorous axiomatic framework for the description of quantum mechanical systems with a large number of degrees of freedom, we show that the nonequilibrium steady state, constructed in the quasifree fermionic system corresponding to the isotropic XY chain in which a finite sample, coupled to two thermal reservoirs at different temperatures, is exposed to a local external magnetic field, is breaking translation invariance and exhibits a strictly positive entropy production rate. Moreover, we prove that there exists a second-order nonequilibrium quantum phase transition with respect to the strength of the magnetic field as soon as the system is truly out of equilibrium.