title: Quantum information-geometry of dissipative quantum phase transitions.
abstract: A general framework for analyzing the recently discovered phase transitions in the steady state of dissipation-driven open quantum systems is still lacking. 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 correlation matrices of steady states with a metric tensor g measuring the distinguishability distance between solutions corresponding to a different set of control parameters. The phase diagram can then be 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 insights into dissipative quantum critical phenomena as well as a general and powerful strategy to explore them.
authors.affiliation: Institute for Scientific Interchange Foundation, Via Alassio 11/c, 10126 Torino, Italy.
authors.forename: Leonardo
authors.initials: L
authors.lastname: Banchi
authors.affiliation: Institute for Scientific Interchange Foundation, Via Alassio 11/c, 10126 Torino, Italy.
authors.forename: Paolo
authors.initials: P
authors.lastname: Giorda
authors.affiliation: Department of Physics and Astronomy, and Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, California 90089-0484, USA and Centre for Quantum Technologies, National University of Singapore, 2 Science Drive 3, Singapore 117542.
authors.forename: Paolo
authors.initials: P
authors.lastname: Zanardi