Document Type

Article

Date of Original Version

1984

Abstract

We present new results on the time‐dependent correlation functions Ξ n (t) =4〈S ξ 0(t)S ξ n 〉, ξ=x,y at zero temperature of the one‐dimensional S=1/2 isotropic X Y model (h=γ=0) and of the transverse Ising model (TI) at the critical magnetic field (h=γ=1). Both models are characterized by special cases of the Hamiltonian H=−J∑ l [(1+γ)S x l S x l+1 +(1−γ)S y l S y l+1 +h S z l ]. We have derived exact results on the long‐time asymptotic expansions of the autocorrelation functions (ACF’s) Ξ0(t) and on the singularities of their frequency‐dependent Fourier transforms Φξξ 0(ω). We have also determined the latter functions by high‐precision numerical calculations. The functions Φξξ 0(ω), ξ=x,y have singularities at the infinite sequence of frequencies ω=mω0, m=0, 1, 2, 3, ... where ω0=J for the X Y model and ω0=2J for the TI model. In both models the singularities in Φ x x 0 (ω) for m=0, 1 are divergent, whereas the nonanalyticities at higher frequencies become increasingly weaker. We point out that the nonanalyticities at ω≠0 are intrinsic features of the discrete quantum chain and have therefore not been found in the context of a continuum analysis.

Publisher Statement

Copyright 1984 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.

The following article appeared in Journal of Applied Physics and may be found at http://dx.doi.org/10.1063/1.333505.

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