High-precision determination of low-energy effective parameters for a two-dimensional Heisenberg quantum antiferromagnet

The two-dimensional (2D) spin-12 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 M_s=0.307 43(1)/a2, the spin stiffness ρ_s=0.180 81(11)J, and the spin wave velocity c=1.6586(3)Ja, are determined with very high precision. Our study may serve as a test case for the comparison of lattice quantum chromodynamics 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.