Efficient quantum information probes of non-equilibrium quantum criticality

Abstract

In this letter we address the problem of detecting phase transitions without prior knowledge of a suitable order parameter. To this end, we propose a notion of metric based on the distance between single-particle covariance matrices. Unlike the well-known fidelity susceptibility, this quantity is accessible to commonly employed numerical techniques and can potentially serve as a versatile instrument to identify phase transitions beyond Landau's paradigm.In particular, we demonstrate that one choice of metric, which we dubbed single-particle affinity and that coincides with the fidelity for quadratic models can identify non-equilibrium phase transitions. This is shown for a boundary-driven fermion chain under Markovian dissipation, that escapes Landau's framework. We also apply this method to a fermion ladder and find a rather rich phase diagram, contrary to what would be expected from preceding related work on spin ladders.