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

Ruggiero, P.
•
Calabrese, P.
2017
  • journal article

Periodico
JOURNAL OF HIGH ENERGY PHYSICS
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 matrices ρ1 and ρ0 of a quantum field theory, we employ the replica trick which relies on the path integral representation of Tr(ρ1ρn−10) and define a set of R\'enyi relative entropies Sn(ρ1‖ρ0). 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. © 2017, The Author(s).
DOI
10.1007/JHEP02(2017)039
WOS
WOS:000394747600002
SCOPUS
2-s2.0-85012031596
Archivio
http://hdl.handle.net/20.500.11767/48273
Diritti
open access
Soggetti
  • Conformal Field Theor...

  • Field Theories in Low...

  • Settore FIS/02 - Fisi...

Web of Science© citazioni
28
Data di acquisizione
Jun 4, 2022
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