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 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.

5+6 pages, 2 figures, presentation improved, new results and references added

References in corpus (13)

• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• An Open-System Quantum Simulator with Trapped Ions
• Quantum critical scaling of the geometric tensors
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Dissipative preparation of entanglement in optical cavities
• Dynamical Phase Transitions and Instabilities in Open Atomic Many-Body Systems
• Quantum phase transition in a far from equilibrium steady state of XY spin chain
• Classifying and measuring the geometry of the quantum ground state manifold
• Quantum phase transitions and quantum fidelity in free fermion graphs
• Dissipative Dynamics and Phase Transitions in Fermionic Systems
• Bures metric over thermal state manifolds and quantum criticality
• Solvable quantum nonequilibrium model exhibiting a phase transition and a matrix product representation
• Long range order in non-equilibrium interacting quantum spin chains

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• Current circulation near additional energy degeneracy points in quadratic Fermionic networks
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