Symmetry Resolved Entanglement of Excited States in Quantum Field Theory II: Numerics, Interacting Theories and Higher Dimensions

TL;DR

This paper extends the analysis of symmetry resolved entanglement in quantum field theories to interacting models and higher dimensions, supported by numerical evidence from lattice theories.

Contribution

It introduces a universal formula for symmetry resolved entanglement in excited states, applicable to interacting theories and higher-dimensional models, with numerical validation.

Findings

Universal ratio of charged moments depends on excitations and symmetry charges

Numerical results confirm the formula in free lattice theories

Extension of the framework to interacting theories and higher dimensions

Abstract

In a recent paper we studied the entanglement content of zero-density excited states in complex free quantum field theories, focusing on the symmetry resolved entanglement entropy (SREE). By zero-density states we mean states consisting of a fixed, finite number of excitations above the ground state in an infinite-volume system. The SREE is defined for theories that possess an internal symmetry and provides a measure of the contribution to the total entanglement of each symmetry sector. In our work, we showed that the ratio of Fourier-transforms of the SREEs (i.e. the ratio of charged moments) takes a very simple and universal form for these states, which depends only on the number, statistics and symmetry charge of the excitations as well as the relative size of the entanglement region with respect to the whole system's size. In this paper we provide numerical evidence for our formulae by computing functions of the charged moments in two free lattice theories: a 1D Fermi gas and a complex harmonic chain. We also extend our results in two directions: by showing that they apply also to excited states of interacting theories (i.e. magnon states) and by developing a higher dimensional generalisation of the branch point twist field picture, leading to results in (interacting) higher-dimensional models.