Monte Carlo Determination of the Low-Energy Constants of a Spin 1/2 Heisenberg Model with Spatial Anisotropy

TL;DR

This study uses Monte Carlo simulations to calculate low-energy constants of a spin 1/2 Heisenberg model with spatial anisotropy, providing insights into magnetic properties relevant for understanding electronic liquid crystal pinning in YBCO.

Contribution

It introduces a first-principles Monte Carlo approach to determine low-energy constants in an anisotropic Heisenberg model, extending previous methods to strong anisotropy regimes.

Findings

Good agreement with series expansion in weak anisotropy

Discrepancies observed in strong anisotropy regime

Spin stiffness varies with coupling ratio

Abstract

Motivated by the possible mechanism for the pinning of the electronic liquid crystal direction in YBCO as proposed in \cite{Pardini08}, we use the first principles Monte Carlo method to study the spin 1/2 Heisenberg model with antiferromagnetic couplings $J_{1}$ and $J_{2}$ on the square lattice. The corresponding low-energy constants, namely the spin stiffness $\rho_s$, the staggered magnetization density ${\cal M}_s$, the spin wave velocity $c$, as well as the ground state energy density $e_0$ are determined by fitting the Monte Carlo data to the predictions of magnon chiral perturbation theory. In particular, the spin stiffnesses $\rho_{s1}$ and $\rho_{s2}$ are investigated as a function of the ratio $J_{2}/J_{1}$ of the couplings. Although we find a good agreement between our results with those obtained by the series expansion method in the weakly anisotropic regime, for strong anisotropy we observe discrepancies.