Entanglement asymmetry in conformal field theory and holography

Abstract

Entanglement asymmetry is a measure of symmetry breaking in quantum subsystems, inspired by quantum information theory, particularly suited to study out-of-equilibrium states. We study the entanglement asymmetry of a class of excited "coherent states" in conformal quantum field theories with a U(1) symmetry, employing Euclidean path-integral methods with topological symmetry defects and the replica formalism. We compute, at leading order in perturbation theory, the asymmetry for a variety of subsystems, including finite spherical subregions in flat space, in finite volume, and at positive temperature. We also study its Lorentzian time evolution, showcasing the dynamical restoration of the symmetry due to thermalization, as well as the presence of a quantum Mpemba effect. Our results are universal, and apply in any number of dimensions. We also show that the perturbative entanglement asymmetry is related to the Fisher information metric, which has a known holographic dual called Hollands-Wald canonical energy, and that it is captured by the AdS bulk charge contained in the entanglement wedge.

29 pages plus appendices, 11 figures; v2: many improvements, figures redone, new app D, refs added; v3: some clarifications, published version

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Cited by in corpus (11)

• The quantum Mpemba effects
• Symmetry restoration and quantum Mpemba effect in many-body localization systems
• A simpler probe of the quantum Mpemba effect in closed systems
• Entanglement asymmetry dynamics in random quantum circuits
• Quantum Mpemba effect in long-range spin systems
• Symmetry breaking in chaotic many-body quantum systems at finite temperature
• Dynamics of entanglement fluctuations and quantum Mpemba effect in the $\nu =1$ QSSEP model
• Quantum Entanglement Index in String Theory
• Quench dynamics of entanglement entropy under projective charge measurements: the free fermion case
• Quantum geometric tensor determines the pure-state i.i.d. conversion rate in the resource theory of asymmetry for any compact Lie group
• Higher-form entanglement asymmetry and topological order