Magnetic Order-Disorder Transition in the Two-Dimensional Spatially Anisotropic Heisenberg Model at Zero Temperature

TL;DR

This study investigates the zero-temperature magnetic phase transition in a two-dimensional anisotropic Heisenberg model, revealing a sharp crossover at a specific coupling ratio using advanced numerical methods.

Contribution

It introduces a combined Green's-function and Lanczos diagonalization approach to analyze the anisotropic Heisenberg model's ground state and identifies a critical coupling ratio for the phase transition.

Findings

Sharp crossover at coupling ratio R0 ≈ 0.2

Transition from Néel to paramagnetic state

Spatial dependence of spin correlations analyzed

Abstract

The ground-state properties of the spin-1/2 antiferromagnetic Heisenberg model with spatially anisotropic couplings on a square lattice are investigated by a spin-rotation-invariant Green's-function approach and by Lanczos diagonalizations on lattices up to 36 sites supplemented by finite-size scaling. We focus on the anisotropy-driven transition from the N\'eel state to a paramagnetic state with antiferromagnetic short-range order and on the spatial dependence of spin correlation functions. Our principal result is that a rather sharp crossover in the magnetic behavior occurs at the coupling ratio $R_0\simeq 0.2$ ($R=J_y/J_x$).