RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


TMF, 2010, Volume 164, Number 3, Pages 363–367 (Mi tmf6545)  

This article is cited in 1 scientific paper (total in 1 paper)

Generalized entropy of the Heisenberg spin chain

A. R. Itsa, V. E. Korepinb

a Department of Mathematical Sciences, Indiana University--Purdue University Indianapolis, Indianapolis, USA
b Yang Institute for Theoretical Physics, State University of New York, Stony Brook, New York, USA

Abstract: We consider the XY quantum spin chain in a transverse magnetic field. We consider the Rényi entropy of a block of neighboring spins at zero temperature on an infinite lattice. the Rényi entropy is essentially the trace of some power $\alpha$ of the density matrix of the block. We calculate the entropy of the large block in terms of Klein's elliptic $\lambda$-function. We study the limit entropy as a function of its parameter $\alpha$. We show that the Rényi entropy is essentially an automorphic function with respect to a certain subgroup of the modular group. Using this, we derive the transformation properties of the Rényi entropy under the map $\alpha\to\alpha^{-1}$.

Keywords: quantum entanglement, spin chain, Bethe ansatz

DOI: https://doi.org/10.4213/tmf6545

Full text: PDF file (354 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2010, 164:3, 1136–1139

Bibliographic databases:


Citation: A. R. Its, V. E. Korepin, “Generalized entropy of the Heisenberg spin chain”, TMF, 164:3 (2010), 363–367; Theoret. and Math. Phys., 164:3 (2010), 1136–1139

Citation in format AMSBIB
\Bibitem{ItsKor10}
\by A.~R.~Its, V.~E.~Korepin
\paper Generalized entropy of the~Heisenberg spin chain
\jour TMF
\yr 2010
\vol 164
\issue 3
\pages 363--367
\mathnet{http://mi.mathnet.ru/tmf6545}
\crossref{https://doi.org/10.4213/tmf6545}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2010TMP...164.1136I}
\transl
\jour Theoret. and Math. Phys.
\yr 2010
\vol 164
\issue 3
\pages 1136--1139
\crossref{https://doi.org/10.1007/s11232-010-0091-6}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000282695500004}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77957985980}


Linking options:
  • http://mi.mathnet.ru/eng/tmf6545
  • https://doi.org/10.4213/tmf6545
  • http://mi.mathnet.ru/eng/tmf/v164/i3/p363

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Sonnino G., Steinbrecher G., “Generalized Extensive Entropies For Studying Dynamical Systems in Highly Anisotropic Phase Spaces”, Phys. Rev. E, 89:6 (2014), 062106  crossref  adsnasa  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:557
    Full text:149
    References:41
    First page:11

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020