Correlation Functions of XX0 Heisenberg Chain, q-Binomial Determinants, and Random Walks

Abstract

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.

27 pages, 2 figures, LaTeX

References in corpus (5)

• Non-intersecting Brownian walkers and Yang-Mills theory on the sphere
• Vicious walk with a wall, noncolliding meanders, and chiral and Bogoliubov-deGennes random matrices
• Contributions to the Theory of the Barnes Function
• Nonintersecting Paths, Noncolliding Diffusion Processes and Representation Theory
• From Vicious Walkers to TASEP

Cited by in corpus (5)

• Correlation Functions as Nests of Self-Avoiding Paths
• Zero Range Process and Multi-Dimensional Random Walks
• Heisenberg XX chain, non-homogeneously parameterised generating exponential, and diagonally restricted plane partitions
• Spin correlation functions, Ramus-like identities, and enumeration of constrained lattice walks and plane partitions
• How to Draw a Correlation Function