Dynamical properties of the isotropic XY model

Abstract

The dynamical longitudinal properties of the isotropic one-dimensional XY model are obtained by the two-time Green function method, which involves 《a + λ a μ |a + ν a σ 》 (7minus;) , 《a + λ a μ |a + ν a σ 》 (+) and 《a μ |a + λ a σ a + λ 》 (+) defined by the anticommulator and the commutator. The frequency-and wave number- dependent susceptibility, the response function and the relaxation function (canonical) correlation function) are obtained and discussed for all temperatures. The imaginary part of the frequency- and wave number-dependent susceptibility diverges at ω=4J sin ( κ 2 ) and vanishes for ω >; 4J sin ( κ 2 ) . The difference between isothermal and zero-frequency isolated susceptibilities is resolved by taking the limit κ →0 χzz ( κ , 0). The contribution of the zero-frequency pole in the two-frequency pole in the two-time Green function is also discussed and clarified.