Quantum Monte Carlo calculation of the long-range order in the Heisenberg antiferromagnet

Abstract

A Green’s-function Monte Carlo (GFMC) method is used to compute the staggered magnetization ${\mathit{m}}^{\mathrm{°}}$ in the two-dimensional, spin-1/2 Heisenberg antiferromagnet on L×L square lattices, up to L=12. Unlike previous GFMC calculations, the present method, which uses the forward-walking algorithm is unbiased and projects out the exact, rotationally invariant ground state. These calculations provide confirmation of the existence of long-range antiferromagnetic order in the ground state. A known relationship between ${\mathit{m}}^{\mathrm{°}}$ and the leading finite-size correction, coupled with high-precision ground-state-energy calculations, is used to reduce the error in extrapolating to the thermodynamic limit. The data extrapolate to ${\mathit{m}}^{\mathrm{°}}$=0.3075±0.0025, only slightly different from the spin-wave-theory result, 0.3034. Several perfect singlet trial wave functions used to reduce the statistical error are discussed. A possible explanation as to why exact-diagonalization extrapolations tend to yield low values of ${\mathit{m}}^{\mathrm{°}}$ is presented.