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 Zap. Nauchn. Sem. POMI, 2018, Volume 473, Pages 66–76 (Mi znsl6654)

The ground state-vector of the $XY$ Heisenberg chain and the Gauss decomposition

N. Bogoliubov, C. Malyshev

St. Petersburg Department of Steklov Institute of Mathematics, RAS Fontanka 27, St. Petersburg, Russia

Abstract: The $XY$ Heisenberg spin$\frac12$ chain is considered in the fermion representation. The construction of the ground state-vector is based on the group-theoretical approach. The exact expression for the ground state-vector will allow to study the combinatorics of the correlation functions of the model.

Key words and phrases: $XY$ Heisenberg spin chain, ground state-vector, Gauss decomposition.

 Funding Agency Grant Number Russian Foundation for Basic Research 16-01-00296_à The work was partially supported by the RFBR project (16-01-00296).

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English version:
Journal of Mathematical Sciences (New York), 2019, 242:5, 628–635

UDC: 517.9
Language:

Citation: N. Bogoliubov, C. Malyshev, “The ground state-vector of the $XY$ Heisenberg chain and the Gauss decomposition”, Questions of quantum field theory and statistical physics. Part 25, Zap. Nauchn. Sem. POMI, 473, POMI, St. Petersburg, 2018, 66–76; J. Math. Sci. (N. Y.), 242:5 (2019), 628–635

Citation in format AMSBIB
\Bibitem{BogMal18} \by N.~Bogoliubov, C.~Malyshev \paper The ground state-vector of the $XY$ Heisenberg chain and the Gauss decomposition \inbook Questions of quantum field theory and statistical physics. Part~25 \serial Zap. Nauchn. Sem. POMI \yr 2018 \vol 473 \pages 66--76 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl6654} \transl \jour J. Math. Sci. (N. Y.) \yr 2019 \vol 242 \issue 5 \pages 628--635 \crossref{https://doi.org/10.1007/s10958-019-04501-9} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85074211453}