Monte Carlo study of a two-dimensional quantum ferromagnet

Abstract

We present quantum Monte Carlo results for the field and temperature dependence of the magnetization and the spin-lattice relaxation rate 1/T1 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 ν = 1 quantum Hall ferromagnet, which is expected to be well described by the Heisenberg model. The dynamic response function needed to extract 1/T1 is obtained using maximum-entropy analytic continuation of the corresponding imaginary-time dependent correlation function. We discuss the reliability of this approach.

The thermodynamic properties of a spin-1/2 Heisenberg ferromagnetic system using Oguchi's method

“…The thermodynamic properties of the magnetic system have been studied by many authors both experimentally [1][2][3][4] and theoretically [5][6][7][8][9][10][11]. Effective field theories generally used to describe these thermodynamic properties.…”

High-Energy Magnon Dispersion and Multimagnon Continuum in the Two-Dimensional Heisenberg Antiferromagnet

“…In order to compute the transverse correlations it is more efficient to apply the field in the x direction, so that the measurements can be carried out with diagonal operators [26]. Hence, we perform two independent simulations for each lattice size.…”

Correlated cluster mean-field theory for spin systems

“…The difference is only that the Ising interaction between neighboring spins in a cluster is replaced by the Heisenberg one, S i · S j , in this case. The temperature dependence of the magnetization m obtained by the CCMF approach is compared with those from the MFT, BPW, the so-called randomphase approximation (RPA), 27,28 Kikuchi's square approximation, 23 and quantum Monte Carlo (QMC) calculations 29,30,31,32 in Fig. 5.…”