Dynamical properties of one-dimensional antiferromagnets: A Monte Carlo study

A combination of world-line quantum Monte Carlo and maximum-entropy methods is used to calculate the dynamic structure factor ${\mathit{S}}_{\mathrm{\alpha }\mathrm{\alpha }}$(q,ω) for one-dimensional antiferromagnets. A comparison to exact results demonstrates that qualitative features of spectra are reproduced, but are broadened. The broadening is frequency dependent with low-frequency features being reproduced most accurately. Peak positions are well described. Results for the Heisenberg model with S≤2 demonstrate the qualitative difference between the dynamics of half-integer and integer spins predicted by Haldane. From the positions of the low-temperature q=π peaks quantitative estimates are produced for the S=1 and 2 gaps. The q=π peak position for S=1 increases with temperature in agreement with experiment. When on-site anisotropy is included for S=1 a gap splitting results that resembles that found for NENP [Ni(${\mathrm{C}}_2$ ${\mathrm{H}}_8$ ${\mathrm{N}}_2$ ${)}_2$ ${\mathrm{NO}}_2$ ${\mathrm{ClO}}_4$].