Out-of-equilibrium transverse field XY chain - non-equilibrium phase transitions, transport, and entanglement*

The generalization of quantum phase transitions to non-equilibrium conditions raises a number of questions, in particular, if and how out-of-equilibrium critical phenomena can be categorized into universality classes, in analogy with thermal equilibrium.

Here we explore the non-equilibrium steady-state of an XY spin chain in a transverse magnetic field coupled at its ends to magnetic thermal reservoirs. We generalize the phase diagram to non-equilibrium conditions obtained by applying a magnetization bias to the reservoirs.

Upon increasing the bias we observe a discontinuous jump of the magnetic order parameter that coincides with a divergent the correlation length. While the first observation is a signature of a first-order transition, in equilibrium, the second arises only for continuous transitions. Thus, our findings show that out-of-equilibrium conditions allow for novel critical phenomena not possible at equilibrium. Moreover, for steady-states with a non-vanishing conductance, the entanglement entropy at the zero temperature was found to have logarithmic corrections that differ from the well-known equilibrium case.