Dynamic correlation functions for one-dimensional quantum-spin systems: New results based on a rigorous approach

We present new results on the time-dependent correlation functions n(t)=4 S0 (t)Sn , =x,y, at zero temperature of the one-dimensional S=12 isotropic XY model (h==0) and of the transverse Ising (TI) model at the critical magnetic field (h==1). Both models are characterized by special cases of the Hamiltonian H=-Jl[(1+)SlxSl+1x+(1-)SlySl+1y+hS1z]. We have derived exact results on the long-time asymptotic expansions of the autocorrelation functions 0(0) and on the singularities of their frequency-dependent Fourier transforms 0 (). We have also determined the latter functions by high-precision numerical calculations. The functions 0 (), =x,y, have singularities at the infinite sequence of frequencies =m0, m=0,1,2,3, , where 0=J for the XY model and 0=2J for the TI model. In the TI case, the leading singularities in 0xx() are alternately one-sided and two-sided power-law singularities, the first two of which (at =0,2J) are divergent. The dominant singularities in the XY case are alternate one-sided power laws and two-sided power laws with logarithmic corrections, the first two of which (at =0,J) are divergent. The singularities at higher frequencies in both models are finite and become increasingly weaker. We point out that the nonanalyticities at 0 are intrinsic features of the discrete quantum chain and have therefore not been found in the context of a continuum analysis (Luttinger model). At least the most prominent features of our new results should be observable in low-temperature dynamical experiments on quasi-one-dimensional compounds such as the XY-like substances Cs2CoCl4 and PrCl3 and the S=12 Ising-like substance CsCoCl3 2H2O.