Monte Carlo study of a two-dimensional quantum ferromagnet

We present quantum Monte Carlo results for the field and temperature dependence of the magnetization and the spin lattice relaxation rate ${1/T}_1$ of a two-dimensional $S=1/2\mathrm{}$ quantum Heisenberg ferromagnet. The Monte Carlo method, which yields results free of systematic errors, is described in detail. The high accuracy of the calculated magnetization allows for stringent tests of recent approximate analytical calculations. We also compare our results with recent experimental data for a $\nu =1\mathrm{}$ quantum Hall ferromagnet, which is expected to be well described by the Heisenberg model. The dynamic response function needed to extract ${1/T}_1$ is obtained using maximum-entropy analytic continuation of the corresponding imaginary-time dependent correlation function. We discuss the reliability of this approach.