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

Journal of High Energy Physics volume 2017, Article number: 39 (2017) Cite this article

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 1∥ρ 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 1∥ρ 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 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.

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  1. International School for Advanced Studies (SISSA) and INFN, Via Bonomea 265, 34136, Trieste, Italy

    Paola Ruggiero & Pasquale Calabrese

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  1. Paola Ruggiero
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  2. Pasquale Calabrese
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Correspondence to Paola Ruggiero.

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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