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Relative entanglement entropies in 1 + 1-dimensional conformal field theories

A preprint version of the article is available at arXiv.

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(ρ 1ρ 0) between two given reduced density matrices ρ 1 and ρ 0 of a quantum field theory, we employ the replica trick which relies on the path integral representation of Tr(ρ 1 ρ n − 10 ) and define a set of Rényi relative entropies S n (ρ 1ρ 0). We compute these quantities for integer values of the parameter n and 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 iϕ, 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.

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Ruggiero, P., Calabrese, P. Relative entanglement entropies in 1 + 1-dimensional conformal field theories. J. High Energ. Phys. 2017, 39 (2017). https://doi.org/10.1007/JHEP02(2017)039

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Keywords

  • Conformal Field Theory
  • Field Theories in Lower Dimensions