Symmetry decomposition of relative entropies in conformal field theory

TL;DR

This paper analyzes the symmetry resolution of relative entropies in a 1+1D free boson CFT with U(1) symmetry, combining analytical replica calculations with numerical lattice tests to validate the theoretical predictions.

Contribution

It introduces a method to compute symmetry resolved relative entropies in CFTs and verifies the results with numerical simulations of the XX spin chain.

Findings

Perfect agreement between CFT predictions and numerical results.

Explicit calculation of symmetry resolved Rènyi relative entropies.

Validation of the replica method for symmetry resolution in CFTs.

Abstract

We consider the symmetry resolution of relative entropies in the 1+1 dimensional free massless compact boson conformal field theory (CFT) which presents an internal $U(1)$ symmetry. We calculate various symmetry resolved R\'enyi relative entropies between one interval reduced density matrices of CFT primary states using the replica method. By taking the replica limit, the symmetry resolved relative entropy can be obtained. We also take the XX spin chain model as a concrete lattice realization of this CFT to perform numerical computation. The CFT predictions are tested against exact numerical calculations finding perfect agreement.