Entanglement asymmetry in conformal field theory and holography

TL;DR

This paper investigates entanglement asymmetry in conformal field theories with U(1) symmetry, revealing universal behavior, its relation to Fisher information, and holographic duals, including symmetry restoration dynamics and quantum effects.

Contribution

It introduces a perturbative method to compute entanglement asymmetry in excited states of conformal field theories and links it to holographic quantities like the Hollands-Wald energy.

Findings

Entanglement asymmetry is computed for various subsystems and states.

The asymmetry relates to Fisher information and holographic energy.

Symmetry is dynamically restored during thermalization, with quantum effects like the Mpemba effect observed.

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.