Rényi entanglement asymmetry in ( 1+1 )-dimensional conformal field theories

In this paper, we consider the Rényi entanglement asymmetry of excited states in the (1+1) dimensional free compact boson conformal field theory (CFT) at equilibrium. We obtain a universal CFT expression written by correlation functions for the charged moments via the replica trick. We provide detailed analytic computations of the second Rényi entanglement asymmetry in the free compact boson CFT for excited states Ψ=Vβ+V−β and Φ=Vβ+J with Vβ and J=i∂ϕ being the vertex operator and current operator, respectively. We make numerical tests of the universal CFT computations using the XX spin chain model. Taking the non-Hermite fake reduced density matrices into consideration, we propose an effective way to test them numerically, which can be applied to other excited states. The CFT predictions are in perfect agreement with the exact numerical calculations. Published by the American Physical Society 2024