Generalized entanglement entropies in two-dimensional conformal field theory

Murciano, Sara; Calabrese, Pasquale; Konik, Robert M.

doi:10.1007/jhep05(2022)152

Title: Generalized entanglement entropies in two-dimensional conformal field theory

Journal Article · 22 May 2022 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep05(2022)152 · OSTI ID:1898587

Murciano, Sara ^[1]; Calabrese, Pasquale ^[2]; Konik, Robert M. ^[3]

International School for Advanced Studies (SISSA), Trieste (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Trieste (Italy)
International School for Advanced Studies (SISSA), Trieste (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Trieste (Italy); International Centre for Theoretical Physics (ICTP), Trieste (Italy)
Brookhaven National Lab. (BNL), Upton, NY (United States). Condensed Matter Physics and Materials Science

We introduce and study generalized Rényi entropies defined through the traces of products of Tr_B(| Ψ_i$$\rangle$$$$\langle$$Ψ_j| ) where |Ψ_i$$\rangle$$ are eigenstates of a two-dimensional conformal field theory (CFT). When |Ψ_i$$\rangle$$ = |Ψ_j$$\rangle$$ these objects reduce to the standard Rényi entropies of the eigenstates of the CFT. Exploiting the path integral formalism, we show that the second generalized Rényi entropies are equivalent to four point correlators. We then focus on a free bosonic theory for which the mode expansion of the fields allows us to develop an efficient strategy to compute the second generalized Rényi entropy for all eigenstates. As a byproduct, our approach also leads to new results for the standard Rényi and relative entropies involving arbitrary descendent states of the bosonic CFT.

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Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: European Research Council (ERC); USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC02-98CH10886; SC0012704

OSTI ID:: 1898587

Report Number(s):: BNL-223703-2022-JAAM

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 5 Vol. 2022; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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