Entanglement entropies of equilibrated pure states in quantum many-body systems and gravity

TL;DR

This paper presents a universal approximation for entanglement entropies in equilibrated pure states of quantum many-body systems and gravity, providing insights into black hole information paradox and replica wormholes.

Contribution

It introduces a universal method to compute entanglement entropies in equilibrated pure states, applicable to gravity systems and black holes, without relying on ensemble averages.

Findings

Provides a consistent prescription for entanglement entropy calculation using Euclidean path integrals.

Derives replica wormholes in fixed Hamiltonian systems, challenging previous ensemble-based assumptions.

Addresses the black hole information paradox by connecting entanglement entropy with unitarity.

Abstract

We develop a universal approximation for the Renyi entropies of a pure state at late times in a non-integrable many-body system, which macroscopically resembles an equilibrium density matrix. The resulting expressions are fully determined by properties of the associated equilibrium density matrix, and are hence independent of the details of the initial state, while also being manifestly consistent with unitary time-evolution. For equilibrated pure states in gravity systems, such as those involving black holes, this approximation gives a prescription for calculating entanglement entropies using Euclidean path integrals which is consistent with unitarity and hence can be used to address the information loss paradox of Hawking. Applied to recent models of evaporating black holes and eternal black holes coupled to baths, it provides a derivation of replica wormholes, and elucidates their mathematical and physical origins. In particular, it shows that replica wormholes can arise in a system with a fixed Hamiltonian, without the need for ensemble averages.