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Relative Entanglement Entropies in 1+1-dimensional conformal field theories

Authors
Paola Ruggiero,Pasquale Calabrese
Stuart Young,Terrance Quinn II,Sunil Mukhi,Vladimir Makarenko,Salahaldin Fathalla,Niklas Beisert,Alessandro Paiella,Richard Jones,Andrzej Wal,Denis Comelli,Зинаида Чеканцева,Vladimir Kulik,Diogo Provete,Mikjel Thorsrud,DIGAMBER PAWAR,Trevor Glasbey,John Platt,Keisuke Yano,Kunal Vyas,Kristen Smith,Lawrence Kennedy,Nenad Đurđević,Luis Emilio Cruz-Barba,Frédéric Dreyer,Dejan Matić,Milivoje Lapčević,Veljko Vlašković,Marko Pavlović,Bojan Urdarević,Zoran Vuković,Zoran Jovanović,Radoje Brković,Alexandru Ciubotaru,Emilija Stanković,Milena Petrović,Jelena Vučković,Ioannis Tsinikos,Tamara Đurđić Milošević,Srđan Vladetić,Jovan Vujičić,Sveto Puríć,Dragica Živojinović, Dj,Dragan Vujisić,Milan Palević,Božin Vlašković,Peter Wolfsteiner,Nenad Janković,Nina Planojević,Milan Rapajić,Slavko Đorđević,Violeta Todorović,Torben Gaedt,Garrett Poe,Vesna Janjić,Jasmina Bogićević,Nada Todorović,Veljko Turanjanin,Vladimir Obradović,Dimitrios Zoakos,Dragan Stojković,Alain Jaccard,Carolyn Dzierba,Mirjana Todorović,Krešimir Kumerički,Biljana Jovković,Marc Torrens,Benjamin Bellenie,Stefan Hoeche,Andy Van Brocklin,Stevan Luković,Srđan Furtula,Luis Garcés-Erice,Joseph Fotsing,Digamber Porob,David Van Wie,Milica Tufegdzic,Dragomir Dimitrijević,Matti Jarvinen,Susana Henriques,N/A ,Jonathan Wall,Marie Connett,Milan Čupić,Miljan Leković,Dejan Jovanović,Bulent Basol,Christopher Herzog,Martin Köhne,David Clarke,Dan Andersen,Kim Landsbergen,Olli Pitkänen,CHIA-HO LIN,Mercedes Medina,Sebastian Linß,Sarah Kraak,Bruno Dufour,Omar Diego Lopez,Eran Palti,Nathaniel Butlin,Isabel María del Águila Cano,Sebastian Rosenbaum,Rafael Maestre,Michele Cicoli,Ingo Jordan,Luiz Agostinho Ferreira,Ivonne Zavala,Nilanjan Brahma,Grigoris Panotopoulos,ALESSANDRO BROGGIO,Engel Roza,Mark Begbie,Diosvany Ortega González,Yukiyoshi Okauchi,Gregory Carven,Stepan Jenicek,Suprabh Prakash,Yue-Lin Sming Tsai,Stuart Haigh,Francesco Riva,Robert LoGalbo,Rong-Chi ,Stephane Coulombe,Alexander Monin,Bruce Bassett,Rafel Escribano,Renee Hlozek,Jose Rubo,Gautam ,Arantza Oyanguren,J. 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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(ρ1ρ0) 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(ρ1ρn1
0 ) and
define a set of Rényi relative entropies Sn(ρ1ρ0). 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.
arXiv:1612.00659v2 [hep-th] 12 Dec 2016
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