Thermodynamic Properties of the Spin-1/2 Heisenberg Antiferromagnet on the Triangular Lattice

Abstract

The Monte Carlo method, which was originally developed for classical systems, has been applied to various quantum systems. In particular, a method based on the generalized Trotter formula has been widely used[1–4]. The Metropolis algorithm for the classical system generates the configurations according to the Boltzmann factor exp(- β )γ ). For a quantum system, it is difficult to calculate the matrix elements of the Boltzmann factor for a large system. It has been shown [1] that the Boltzmann factor can be estimated approximately by using the generalized Trotter formula. One can then map the quantum system into some classical system, in which one can use the Metropolis algorithm. The simulation of this transformed classical system is different from the simulation of usual classical systems in several respects: (1) The transformed classical system has special interaction, or in other words, conservation laws. We need special care for the spin flips to consider the ergodicity. (2) There is a possibility for the Boltzmann factor of the transformed classical system to become negative.