Continuum-limit correlation functions for the spin-one anisotropic Heisenberg chain

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Abstract
The authors derive a continuum representation of the spin-one operators which provides the mapping of the spin-one anisotropic Heisenberg chain onto the Luttinger model. They show a schematic phase diagram of the Hamiltonian, and calculate a general two-spin dynamic correlation function at finite temperatures, valid in the massless domain of the Hamiltonian. This can be applied to obtain the transverse dynamic form factor, and results are compared with neutron scattering data on CsNiF3. The behaviour of the transverse correlation function is shown to be governed by a critical exponent eta u+or- which is a measured of quantum effects in the system, eta M+or- to 0 being the classical limit. Existing data on CsNiF3 are shown to be in the classical regime, and they make suggestions for further experiments to search for quantum fluctuations. They also indicate the limits of applicability of the quantum sine-Gordon theory to CsNIF3.