Very High Precision Determination of Low-Energy Parameters: The 2-d Heisenberg Quantum Antiferromagnet as a Test Case

TL;DR

This paper precisely determines low-energy parameters of the 2D Heisenberg antiferromagnet using Monte Carlo simulations and effective field theory, providing a benchmark for testing analytic predictions against numerical data.

Contribution

The study achieves very high precision in extracting low-energy parameters of the 2D Heisenberg model, serving as a test case for lattice QCD and chiral effective theories.

Findings

Staggered magnetization density ${ m M}_s$ measured as 0.30743(1)/a^2

Spin stiffness $ ho_s$ determined as 0.18081(11) J

Spin wave velocity $c$ found to be 1.6586(3) J a

Abstract

The 2-d spin 1/2 Heisenberg antiferromagnet with exchange coupling $J$ is investigated on a periodic square lattice of spacing $a$ at very small temperatures using the loop-cluster algorithm. Monte Carlo data for the staggered and uniform susceptibilities are compared with analytic results obtained in the systematic low-energy effective field theory for the staggered magnetization order parameter. The low-energy parameters of the effective theory, i.e.\ the staggered magnetization density ${\cal M}_s = 0.30743(1)/a^2$, the spin stiffness $\rho_s = 0.18081(11) J$, and the spin wave velocity $c = 1.6586(3) J a$ are determined with very high precision. Our study may serve as a test case for the comparison of lattice QCD Monte Carlo data with analytic predictions of the chiral effective theory for pions and nucleons, which is vital for the quantitative understanding of the strong interaction at low energies.