Talk page
Title:
Random walks, plane partitions and correlation functions of Heisenberg chain in the limiting cases.
Speaker:
Abstract:
Relations between quantum integrable models and some aspects of enumerative combinatorics and the theory of partitions are discussed. The main example is the Heisenberg XXZ spin chain in the limit cases of zero and infinite anisotropy. 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. We provide a combinatorial interpretation of the formula for the correlation functions in terms of nests of the self-avoiding lattice paths. The interpretation proposed is in turn related to enumeration of the boxed plane partitions. The asymptotic behavior of the correlation functions is studied in the case of a large number of sites and a moderately large number of spin excitations. For sufficiently low temperature a relation is established between the correlation functions and the theory of matrix integrals.
Link:
Workshop: