A determination of the low energy parameters of the 2-d Heisenberg antiferromagnet

TL;DR

This paper uses advanced numerical simulations to precisely determine key low energy parameters of the 2D antiferromagnetic quantum Heisenberg model, aligning well with experimental data for high-temperature superconductor precursors.

Contribution

The study provides the first highly accurate numerical estimates of the low energy parameters of the 2D Heisenberg antiferromagnet using an efficient cluster algorithm and comparison with chiral perturbation theory.

Findings

Ground state energy density: -0.6693(1) J/a^2

Staggered magnetization: 0.3074(4)/a^2

Spin wave velocity: 1.68(1) J a

Abstract

We perform numerical simulations of the 2-d antiferromagnetic quantum Heisenberg model using an efficient cluster algorithm. Comparing the finite size and finite temperature effects of various quantities with recent results from chiral perturbation theory we are able to determine the low energy parameters of the system very precisely. We find $e_0 = - 0.6693(1) J/a^2$ for the ground state energy density, ${\cal M}_s = 0.3074(4)/a^2$ for the staggered magnetization, $\hbar c = 1.68(1) J a$ for the spin wave velocity and $\rho_s = 0.186(4) J$ for the spin stiffness. Our results agree with experimental data for the undoped precursor insulators of high-$T_c$ superconductors.