Quantum Monte Carlo and transfer-matrix calculations for one-dimensional easy-plane ferromagnets.

Abstract

We have applied previously used quantum Monte Carlo (QMC) techniques to obtain numerically the thermodynamics of two well-studied quasi-one-dimensional (1D) easy-plane ferromagnetic models, in the presence of an applied magnetic field in the easy plane. The checkerboard decomposition form of the Trotter approximation to the partition function has been used. Internal energy, specific heat, magnetization, and susceptibility have been obtained for model Hamiltonians believed appropriate for spin S=(1/2) [(${\mathrm{C}}_{6}$${\mathrm{H}}_{11}$${\mathrm{NH}}_{3}$)${\mathrm{CuBr}}_{3}$ (CHAB)] and S=1 (${\mathrm{CsNiF}}_{3}$), in temperature and field ranges where classical theories have predicted solitonlike kink excitations. The S=(1/2) QMC calculations are verified and superseded by a numerically exact quantum transfer-matrix (QTM) technique. Results for the temperature dependence of the peak in the specific heat versus field are compared with available experimental results. For the model applicable to CHAB, it is found that there is no value of the easy-plane anisotropy parameter from 4% to 10% for which the QTM calculation can adequately reproduce the experimentally obtained peak height and position. On the other hand, the QMC results for the model assumed for ${\mathrm{CsNiF}}_{3}$ do roughly reproduce the temperature dependence of the experimental peak positions, but not the peak heights. However, statistical errors present in our QMC data are large, and a better method is still needed for computing the quantum statistical mechanics of S=1 systems.