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Zap. Nauchn. Sem. POMI, 2017, Volume 465, Pages 27–45 (Mi znsl6529)  

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

Correlation functions as nests of self-avoiding paths

N. Bogoliubovab, C. Malyshevab

a St. Petersburg Department of Steklov Institute of Mathematics, RAS, Russia
b ITMO University, Russia

Abstract: We discuss connection between the $XXZ$ Heisenberg spin chain in the limiting case of zero anisotropy and some aspects of enumerative combinatorics. The representation of the Bethe wave functions via the Schur functions allows to apply the theory of symmetric functions to calculation of the correlation functions. We provide a combinatorial derivation of the dynamical correlation functions of the projection operator in terms of nests of self-avoiding lattice paths.

Key words and phrases: Heisenberg spin chain, correlation functions, enumerative combinatorics, Schur functions.

Funding Agency Grant Number
Russian Science Foundation 16-11-10218
The work was supported by Russian Science Foundation (grant no. 16-11-10218).


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English version:
Journal of Mathematical Sciences (New York), 2019, 238:6, 779–792

UDC: 517.9
Received: 06.12.2017
Language:

Citation: N. Bogoliubov, C. Malyshev, “Correlation functions as nests of self-avoiding paths”, Questions of quantum field theory and statistical physics. Part 24, Zap. Nauchn. Sem. POMI, 465, POMI, St. Petersburg, 2017, 27–45; J. Math. Sci. (N. Y.), 238:6 (2019), 779–792

Citation in format AMSBIB
\Bibitem{BogMal17}
\by N.~Bogoliubov, C.~Malyshev
\paper Correlation functions as nests of self-avoiding paths
\inbook Questions of quantum field theory and statistical physics. Part~24
\serial Zap. Nauchn. Sem. POMI
\yr 2017
\vol 465
\pages 27--45
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6529}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2019
\vol 238
\issue 6
\pages 779--792
\crossref{https://doi.org/10.1007/s10958-019-04275-0}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. Bogoliubov, C. Malyshev, “The phase model and the norm-trace generating function of plane partitions”, J. Stat. Mech.-Theory Exp., 2018, 083101  crossref  mathscinet  isi  scopus
  • Записки научных семинаров ПОМИ
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