Steady-state solution for one-dimensional-open-quantum systems*

The generalization of quantum phase transitions into non-equilibrium conditions raises several questions. In particular, how to classify the out-of-equilibrium critical phenomena into universality classes, in analogy with thermal equilibrium?

Here, we explore the non-equilibrium steady-state of one-dimensional systems coupled at its ends to reservoirs. Upon increasing the bias difference between both reservoirs, we draw a phase diagram under non-equilibrium conditions. From an exact approach, we characterize the phase transitions through the order parameter and the correlation length.

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 have logarithmic corrections that differ from the well-known equilibrium case.