Theoretical Physics Seminar:
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Aug 15, 2007 11:00 AM, Theoretical Physics Seminar Room, LC.3.17
Factorization of static correlation functions in the XXZ chain
Speaker: Goehmann, Frank
Abstract: I report on the status of our work on spatial correlation function of the XXZ spin chain. We study spatial correlations by means of the density matrix of a finite segment of the chain. In two cases we succeeded to derive a multiple integral representation for this density matrix: 1) for the infinite chain subject to a heat bath and to an external longitudinal magnetic field, and 2) for the ground state of the finite chain with twisted periodic boundary conditions. We are now studying the multiple integrals in order to obtain explicit results that can be compared with experiments and in order to understand the general structure of all static correlation functions in the spin chain. Using the insight gained for the ground state by Boos, Jimbo, Miwa, Slavnov and Takeyama and combining it with explicit calculations on the multiple integrals and with the high temperature expansion technique we were able to conjecture an explicit exponential formula for the density matrix in case 1). Since the magnetic field is included it yields new formula even in the zero temperature limit. Our conjecture implies that all static correlation functions of the XXZ chain should be polynomials in only two transcendental functions and their derivatives with coefficients of purely algebraic origin.
