The manifold of ground states of a family of quantum Hamiltonians can be endowed with a quantum geometric tensor whose singularities signal quantum phase transitions and give a general way to define quantum phases. In this paper, we show that the same information-theoretic and geometrical approach can be used to describe the geometry of quantum states away from equilibrium. We construct the quantum geometric tensor Qμν for ensembles of states that evolve in time and study its phase diagram and equilibration properties. If the initial ensemble is the manifold of ground states, we show that the phase diagram is conserved, that the geometric tensor equilibrates after a quantum quench, and that its time behavior is governed by out-of-time-order commutators (OTOCs).We finally demonstrate our results in the exactly solvable Cluster-XY model.

Quantum geometric tensor away from equilibrium / Rattacaso, Davide; Vitale, Patrizia; Hamma, Alioscia. - In: JOURNAL OF PHYSICS COMMUNICATIONS. - ISSN 2399-6528. - 4:5(2020), p. 055017. [10.1088/2399-6528/ab9505]

Quantum geometric tensor away from equilibrium

Rattacaso, Davide;Vitale, Patrizia;Hamma, Alioscia
2020

Abstract

The manifold of ground states of a family of quantum Hamiltonians can be endowed with a quantum geometric tensor whose singularities signal quantum phase transitions and give a general way to define quantum phases. In this paper, we show that the same information-theoretic and geometrical approach can be used to describe the geometry of quantum states away from equilibrium. We construct the quantum geometric tensor Qμν for ensembles of states that evolve in time and study its phase diagram and equilibration properties. If the initial ensemble is the manifold of ground states, we show that the phase diagram is conserved, that the geometric tensor equilibrates after a quantum quench, and that its time behavior is governed by out-of-time-order commutators (OTOCs).We finally demonstrate our results in the exactly solvable Cluster-XY model.
2020
Quantum geometric tensor away from equilibrium / Rattacaso, Davide; Vitale, Patrizia; Hamma, Alioscia. - In: JOURNAL OF PHYSICS COMMUNICATIONS. - ISSN 2399-6528. - 4:5(2020), p. 055017. [10.1088/2399-6528/ab9505]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/836665
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