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

Karl J. Runge
Phys. Rev. B 45, 7229 – Published 1 April 1992
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Abstract

A Green’s-function Monte Carlo (GFMC) method is used to compute the staggered magnetization m° 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 m° 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 m°=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 m° is presented.

  • Received 24 June 1991

DOI:https://doi.org/10.1103/PhysRevB.45.7229

©1992 American Physical Society

Authors & Affiliations

Karl J. Runge

  • Lawrence Livermore National Laboratory, University of California, Livermore, California 94550

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Issue

Vol. 45, Iss. 13 — 1 April 1992

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