Mixed-order symmetry-breaking quantum phase transition far from equilibrium

TL;DR

This paper investigates a non-equilibrium phase transition in a quantum spin chain coupled to thermal reservoirs, revealing a mixed-order transition with unique entanglement properties and critical phenomena absent at equilibrium.

Contribution

It demonstrates a novel mixed-order quantum phase transition far from equilibrium, characterized by a discontinuous order parameter jump and divergence of correlation length.

Findings

Discontinuous jump in magnetic order parameter with increasing magnetization bias

Divergence of correlation length at the transition point

Bias-dependent logarithmic correction to entanglement entropy

Abstract

We study the current-carrying steady-state of a transverse field Ising chain coupled to magnetic thermal reservoirs and obtain the non-equilibrium phase diagram as a function of the magnetization potential of the reservoirs. Upon increasing the magnetization bias we observe a discontinuous jump of the magnetic order parameter that coincides with a divergence of the correlation length. For steady-states with a non-vanishing conductance, the entanglement entropy at zero temperature displays a bias dependent logarithmic correction that violates the area law and differs from the well-known equilibrium case. Our findings show that out-of-equilibrium conditions allow for novel critical phenomena not possible at equilibrium.