Steklov Institute of Mathematics at St.Petersburg

PREPRINT 7/2002

XX HEISENBERG SPIN CHAIN AND AN EXAMPLE OF PATH INTEGRAL WITH ``AUTOMORPHIC'' BOUNDARY CONDITIONS

This preprint was accepted March 28, 2002
Contact: C.Malyshev

ABSTRACT:
New representation for the generating function of correlators of
third components of spins in the $XX$ Heisenberg spin chain is
considered in the form given by the fermionic Gaussian path
integrals. A part of the discrete anti-commuting integration
variables is subjected to
``automorphic'' boundary conditions in respect of imaginary time.
The situation when only a part of the integration variables is
subjected to the unusual boundary conditions generalizes more
conventional ones when ``automorphic'' boundary conditions appear
for all sites in the lattice spin models. The results of the
functional integration are expressed in the form of determinants
of the matrix operators. The generating function, as well as the
partition function of the model, are calculated by means of
zeta-regularization. Certain correlation functions at nonzero
temperature are obtained explicitly.