Page curve and symmetries

TL;DR

This paper models black hole evaporation using a qubit system with random dynamics, analyzing symmetry-resolved entropies to understand symmetry effects and symmetry breaking during the process.

Contribution

It introduces a toy model that computes symmetry-resolved entropies and derives an analogue of the Page curve for both conserved and broken symmetry cases.

Findings

Symmetry-resolved entropies reveal features of black hole evaporation.

Derived a symmetry-resolved Page curve.

Showed effects of symmetry breaking on entropy dynamics.

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.