Quantum information-geometry of dissipative quantum phase transitions

TL;DR

This paper develops a geometric framework using fidelity to analyze dissipative quantum phase transitions in open systems, providing new insights into their critical behavior.

Contribution

It extends the fidelity approach to Gaussian Fermionic steady states, enabling a geometric analysis of dissipative quantum phase transitions.

Findings

Manifold of steady states equipped with a distinguishability metric

Mapping phase diagrams via metric scaling behavior

Connections established between metric, Liouvillean gap, and correlation functions

Abstract

A general framework for analyzing the recently discovered phase transitions in the steady state of dissipation-driven open quantum systems is still missing. In order to fill this gap we extend the so-called fidelity approach to quantum phase transitions to open systems whose steady state is a Gaussian Fermionic state. We endow the manifold of correlations matrices of steady-states with a metric tensor g measuring the distinguishability distance between solutions corresponding to different set of control parameters. The phase diagram can be then mapped out in terms of the scaling-behavior of g and connections with the Liouvillean gap and the model correlation functions unveiled. We argue that the fidelity approach, thanks to its differential-geometric and information-theoretic nature, provides novel insights on dissipative quantum critical phenomena as well as a general and powerful strategy to explore them.