Symmetry Resolved Entanglement of Excited States in Quantum Field Theory I: Free Theories, Twist Fields and Qubits

TL;DR

This paper investigates the symmetry-resolved entanglement in excited states of 1+1D free quantum field theories with internal symmetry, revealing universal formulas for charged moments and entanglement entropy using form factor techniques.

Contribution

It introduces universal formulas for symmetry-resolved entanglement in excited states of free theories with internal symmetry, extending previous results to include symmetry charge dependence.

Findings

Universal ratio of charged moments for excited states

Explicit formulas for symmetry resolved entanglement entropy in free theories

Applicability to simple qubit states

Abstract

The excess entanglement resulting from exciting a finite number of quasiparticles above the ground state of a free integrable quantum field theory has been investigated quite extensively in the literature. It has been found that it takes a very simple form, depending only on the number of excitations and their statistics. There is now mounting evidence that such formulae also apply to interacting and even higher-dimensional quantum theories. In this paper we study the entanglement content of such zero-density excited states focusing on the symmetry resolved entanglement, that is on 1+1D quantum field theories that possess an internal symmetry. The ratio of charged moments between the excited and grounds states, from which the symmetry resolved entanglement entropy can be obtained, takes a very simple and universal form, which in addition to the number and statistics of the excitations, now depends also on the symmetry charge. Using form factor techniques, we obtain both the ratio of moments and the symmetry resolved entanglement entropies in complex free theories which possess $U(1)$ symmetry. The same formulae are found for simple qubit states.