Correlation functions of XX0 Heisenberg chain, q-binomial determinants, and random walks

The XX0 Heisenberg model on a cyclic chain is considered. The representation of the Bethe wave functions via the Schur functions allows to apply the well-developed theory of the symmetric functions to the calculation of the thermal correlation functions. The determinantal expressions of the form-fac...

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Bibliographic Details
Published in:Nuclear physics. B 2014-02, Vol.879, p.268-291
Main Authors: Bogoliubov, N.M., Malyshev, C.
Format: Article
Language:English
Subjects:
Boxed plane partition
q-binomial determinant
Random walks
Schur function
XX0 Heisenberg chain
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Summary:The XX0 Heisenberg model on a cyclic chain is considered. The representation of the Bethe wave functions via the Schur functions allows to apply the well-developed theory of the symmetric functions to the calculation of the thermal correlation functions. The determinantal expressions of the form-factors and of the thermal correlation functions are obtained. The q-binomial determinants enable the connection of the form-factors with the generating functions both of boxed plane partitions and of self-avoiding lattice paths. The asymptotical behavior of the thermal correlation functions is studied in the limit of low temperature provided that the characteristic parameters of the system are large enough.
ISSN:0550-3213
1873-1562
DOI:10.1016/j.nuclphysb.2013.12.010