Relative Entanglement Entropies in 1+1-dimensional conformal field theories Paola Ruggiero and Pasquale Calabrese International School for Advanced Studies (SISSA) and INFN, Via Bonomea 265, 34136, Trieste, Italy E-mail:paola.ruggiero@sissa.it,calabrese@sissa.it Abstract:We study the relative entanglement entropies of one interval between excited states of a 1+1 dimensional conformal field theory (CFT). To compute the relative entropy S(ρ1‖ρ0)between two given reduced density matricesρ1andρ0of a quantum field theory, we employ the replica trick which relies on the path integral representation ofTr(ρ1ρn−1 0)and define a set of Rényi relative entropiesSn(ρ1‖ρ0). We compute these quantities for integer values of the parameternand derive via the replica limit, the relative entropy between excited states generated by primary fields of a free massless bosonic field. In particular, we provide the relative entanglement entropy of the state described by the primary operator i∂φ, both with respect to the ground state and to the state generated by chiral vertex operators.These predictions are tested against exact numerical calculations in the XX spin-chain finding perfect agreement. arXiv:1612.00659v2 [hep-th] 12 Dec 2016
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