Date of Original Version
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.
Müller, G., & Shrock, R. E.. Dynamical correlation functions for one-dimensional quantum spin systems: new results based on a rigorous approach. J. Appl. Phys. 55 (1984), 1874-1876.
Available at: http://dx.doi.org/10.1063/1.333505