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

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 ${\mathcal{M}}_s$, 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.

4 pages, 4 figures, version accepted for publishing in Phys. Rev. B

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• Electronic liquid crystal state in the high-temperature superconductor YBCO(6.45)
• Spin dynamics in the pseudogap state of a high-temperature superconductor
• In-plane anisotropy of spin excitations in the normal and superconducting states of underdoped YBa${}_2$Cu${}_3$O${}_{6+x}$
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• Subtlety of Determining the Critical Exponent $\nu$ of the Spin-1/2 Heisenberg Model with a Spatially Staggered Anisotropy on the Honeycomb Lattice
• Quantum phase transitions of multi-species Dirac fermions
• Universal scalings of Néel temperature, staggered magnetization density, and spinwave velocity of three-dimensional disordered and clean quantum antiferromagnets
• Monte Carlo determination of the low-energy constants for a two-dimensional spin-1 Heisenberg model with spatial anisotropy