High-temperature dynamics of the anisotropic Heisenberg chain studied by moment methods

Abstract

The dynamics of the anisotropic spin-l/2 nearest-neighbour Heisenberg chain is studied at infinite temperature. Low-order coefficients of the short-time expansions are computed for spin-spin and energy-density-energy-density correlation functions for cyclical as well as for open-ended chains. The commutator algebra necessary to generate these coefficients may be performed by a computer. The series obtained for the spin correlation function (up to order t^14 for a bulk spin and up to order t^18 for a boundary spin) and for the energy density correlation function are the longest ones available up to now. The coefficients are used to construct rigorous upper and lower bounds to autocorrelation functions and near-neighbour correlation functions.