Monte Carlo study of a two-dimensional quantum ferromagnet

TL;DR

This study uses quantum Monte Carlo simulations to analyze the magnetization and relaxation rates of a two-dimensional quantum Heisenberg ferromagnet, providing high-accuracy results that test analytical models and compare with experimental data.

Contribution

It offers detailed quantum Monte Carlo results for a 2D quantum ferromagnet, including dynamic response functions, with validation against analytical and experimental findings.

Findings

High-accuracy magnetization data for the 2D quantum ferromagnet.

Comparison of Monte Carlo results with analytical calculations.

Agreement with experimental data on quantum Hall ferromagnets.

Abstract

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 $S=1/2$ 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 $\nu=1$ 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.