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Zap. Nauchn. Sem. POMI, 2019, Volume 487, Pages 53–67 (Mi znsl6902)  

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

Enumerative combinatorics of $XX0$ Heisenberg chain

N. M. Bogoliubov

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, 27 Fontanka, St. Petersburg 191023, Russia

Abstract: In the present paper the enumeration of a certain class of directed lattice paths is based on the analysis of dynamical correlation functions of the exactly solvable $XX0$ model. This model is the zero anisotropy limit of one of the basic models of the theory of integrable systems, the $XXZ$ Heisenberg magnet. We demonstrate that the considered correlation functions under different boundary conditions are the exponential generating functions of the different types of paths, Dyck and Motzkin in particular.

Key words and phrases: $XX0$ Heisenberg chain, correlation functions, directed lattice paths, generating functions.

Funding Agency Grant Number
Russian Foundation for Basic Research 19-01-00311
Supported in part by RFBR 19-01-00311.


Full text: PDF file (246 kB)
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UDC: 517.9
Received: 21.11.2019
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Citation: N. M. Bogoliubov, “Enumerative combinatorics of $XX0$ Heisenberg chain”, Questions of quantum field theory and statistical physics. Part 26, Zap. Nauchn. Sem. POMI, 487, POMI, St. Petersburg, 2019, 53–67

Citation in format AMSBIB
\Bibitem{Bog19}
\by N.~M.~Bogoliubov
\paper Enumerative combinatorics of $XX0$ Heisenberg chain
\inbook Questions of quantum field theory and statistical physics. Part~26
\serial Zap. Nauchn. Sem. POMI
\yr 2019
\vol 487
\pages 53--67
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6902}


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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. M. Bogoliubov, C. L. Malyshev, “Heisenberg $XX0$ chain and random walks on a ring”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 27, Zap. nauchn. sem. POMI, 494, POMI, SPb., 2020, 48–63  mathnet
  • Записки научных семинаров ПОМИ
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