Page curve and symmetries

Abstract

Motivated by the quantum process of black hole evaporation and its implications for symmetries, we consider a qubit system with a random dynamics as a toy model of black hole. We compute its symmetry-resolved entropies and discuss its implications. We first consider the case where charges are conserved and compute the symmetry-resolved entropies. We derive a symmetry-resolved analogue of the Page curve. We then consider the case where symmetry is explicitly broken and charges are no longer conserved. It serves as a toy model for global symmetry breaking in black hole evaporation. Despite the simple framework, the symmetry-resolved entropies capture various interesting features during the analogous process of black hole evaporation in our qubit model.

7 pages, 4 figures

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• Free-fermion Page Curve: Canonical Typicality and Dynamical Emergence
• Page curve entanglement dynamics in an analytically solvable model
• Non-abelian symmetry-resolved entanglement entropy
• Symmetry breaking in chaotic many-body quantum systems at finite temperature
• Non-Abelian entanglement asymmetry in random states
• Symmetry classification of typical quantum entanglement
• Subsystem Trace-Distances of Two Random States
• Symmetry-resolved genuine multi-entropy: Haar random and graph states
• Additional quantum many-body scars of the spin-$1$ $XY$ model with Fock-space cages and commutant algebras