Typical entanglement entropy with charge conservation

TL;DR

This paper derives a universal formula for the typical entanglement entropy in many-body systems with fixed charge, applicable to various symmetries and representations, linking it to local thermal entropy.

Contribution

It introduces a general formula for entanglement entropy with charge conservation, applicable to both abelian and non-abelian symmetries, including reducible representations.

Findings

The entanglement entropy can be expressed in terms of local thermal entropy at fixed charge density.

The formula applies to systems with U(1) and SU(2) symmetries, including reducible representations.

Illustrations with model systems demonstrate the formula's relevance to quantum chaos.

Abstract

We consider a many-body Hilbert space with a fixed global charge and show that the typical entanglement entropy of a subsystem, at the leading and subleading order in the thermodynamic limit, can be expressed in terms of a single quantity which represents the local thermal entropy at fixed charge density. We find a general formula which applies both to abelian U(1) symmetry and non-abelian SU(2) symmetry, including the case of a local Hilbert space which transforms under a general reducible representation of the symmetry group. We illustrate the general formula with model systems and discuss the relevance of the results as a probe of quantum chaos for physical Hamiltonians.