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Quantum information-geometry of dissipative quantum phase transitions

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.