Symmetry decomposition of relative entropies in conformal field theory

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 Renyi 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.

Automated summary

In this study, we investigate the symmetry resolution of relative entropies in the 1+1 dimensional free massless compact boson conformal field theory with internal U(1) symmetry. By calculating various symmetry resolved Renyi relative entropies and taking the replica limit, we obtain the symmetry resolved relative entropy. Numerical computations using the XX spin chain model confirm the perfect agreement between CFT predictions and exact numerical calculations.