Quantitative description of long-range order in the anisotropic spin-1/2 Heisenberg antiferromagnet on the square lattice

TL;DR

This paper provides a comprehensive quantitative analysis of long-range order in the anisotropic spin-1/2 Heisenberg antiferromagnet on the square lattice using both quantum Monte Carlo simulations and semi-analytic methods, covering the full parameter range.

Contribution

It offers the first combined validation of QMC and semi-analytic approaches for this model across all anisotropy parameters, including analytical relations between dispersion and correlation length.

Findings

Validated the applicability of both methods across the entire parameter range.

Provided quantitative reference results for ground-state properties in the thermodynamic limit.

Derived an analytical relation between dispersion and correlation length at zero temperature.

Abstract

The quantitative description of long-range order remains a challenge in quantum many-body physics. We provide zero-temperature results from two complementary methods for the ground-state energy per site, the sublattice magnetization, the spin gap, and the transverse spin correlation length for the spin-1/2 anisotropic quantum Heisenberg antiferromagnet on the square lattice. On the one hand, we use exact, large-scale quantum Monte Carlo (QMC) simulations. On the other hand, we use the semi-analytic approach based on continuous similarity transformations in terms of elementary magnon excitations. Our findings confirm the applicability and quantitative validity of both approaches along the full parameter axis from the Ising point to the symmetry-restoring phase transition at the Heisenberg point and further provide quantitative reference results in the thermodynamic limit. In addition, we analytically derive the relation between the dispersion and the correlation length at zero temperature in arbitrary dimension, and discuss improved second-moment QMC estimators.