Uhlmann curvature in dissipative phase transitions

TL;DR

This paper investigates how the mean Uhlmann curvature signals phase transitions in dissipative fermionic systems, revealing its potential as a criticality indicator independent of the Liouvillian gap.

Contribution

It demonstrates that the Uhlmann curvature's singular behavior indicates criticality in non-equilibrium steady states of open fermionic systems, providing a new criterion for phase transitions.

Findings

Uhlmann curvature diverges at critical points in the thermodynamic limit.

Finite-size scaling of Uhlmann curvature accurately maps phase diagrams.

Relation established between Uhlmann curvature and dissipative gap.

Abstract

We study the mean Uhlmann curvature in fermionic systems undergoing a dissipative driven phase transition. We consider a paradigmatic class of lattice fermion systems in non-equilibrium steady-state of an open system with local reservoirs, which are characterised by a Gaussian fermionic steady state. In the thermodynamical limit, in systems with translational invariance we show that a singular behaviour of the Uhlmann curvature represents a sufficient criterion for criticalities, in the sense of diverging correlation length, and it is not otherwise sensitive to the closure of the Liouvillian dissipative gap. In finite size systems, we show that the scaling behaviour of the mean Uhlmann curvature maps faithfully the phase diagram, and a relation to the dissipative gap is put forward. We argue that the mean Uhlmann phase can shade light upon the nature of non equilibrium steady state criticality in particular with regard to the role played by quantum vs classical fluctuations.