Ordered moment in the anisotropic and frustrated square lattice Heisenberg model

TL;DR

This study investigates how spatial exchange anisotropy influences magnetic order in the frustrated square lattice Heisenberg model, revealing that anisotropy stabilizes the columnar antiferromagnetic phase across various frustration levels.

Contribution

It introduces a systematic finite size scaling method for the anisotropic J_1a,b-J_2 model using exact diagonalization, extending understanding of magnetic phases in frustrated systems.

Findings

Exchange anisotropy stabilizes the columnar antiferromagnetic phase.

Finite size scaling method compatible with magnetic phases.

Anisotropy suppresses the spin nematic phase.

Abstract

The two-dimensional frustrated next nearest neighbor Heisenberg model on the square lattice is a prime example for a spin system where quantum fluctuations can either destroy or stabilize magnetic order. The phase boundaries and staggered moment dependence on the frustration ratio J_2/J_1 of the exchange constants are fairly well understood both from approximate analytical and numerical methods. In this work we use exact diagonalization for finite clusters for an extensive investigation of the more general J_1a,b-J_2 model which includes a spatial exchange anisotropy between next-neighbor spins. We introduce a systematic way of tiling the square lattice and, for this low symmetry model, define a controlled procedure for the finite size scaling that is compatible with the possible magnetic phases. We obtain ground state energies, structure factors and ordered moments and compare with the results of spin wave calculations. We conclude that J_1a,b exchange anisotropy strongly stabilizes the columnar antiferromagnetic phase for all frustration parameters, in particular in the region of the spin nematic phase of the isotropic model.