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Physical review. B, Condensed matter

Ground-state staggered magnetization of the antiferromagnetic Heisenberg model

O. Haan, J.-U. Klaetke, K.-H. Mütter

Published Sep 1, 1992• 12 citations
Publisher

Abstract

Using helical boundary conditions, we present exact-diagonalization results for two-dimensional spin-1/2 antiferromagnetic Heisenberg systems. Energy and staggered magnetization for an infinite system are obtained by extrapolation from finite square systems. Comparisons with the results obtained for periodic boundary conditions are made.
DOI
10.1103/physrevb.46.5723

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The ground-state energy, staggered magnetization, and correlation function are computed for the two-dimensional spin-(1/2 quantum antiferromagnetic Heisenberg model (believed to be relevant to the high-temperature superconducting materials without doping) on lattices up to 24\ifmmode\times\else\texttimes\fi{}24 by Monte Carlo methods extrapolated to zero temperature. A more accurate value for the ground-state energy is determined by the method of Neumann and Ulam by extrapolating from lattices up to 12\ifmmode\times\else\texttimes\fi{}12.
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We present numerical exact results for the ground state and the low-lying excitations for the spin-1/2 J1-J2 Heisenberg antiferromagnet on finite square lattices of up to N = 40 sites. Using finite-size extrapolation we determine the ground-state energy, the magnetic order parameters, the spin gap, the uniform susceptibility, as well as the spin-wave velocity and the spin stiffness as functions of the frustration parameter J2/J1. In agreement with the generally excepted scenario we find semiclassical magnetically ordered phases for J2 < J c1 2 and J2> J c2 2 separated by a gapful quantum paramagnetic phase. We estimate Jc1 2 ≈ 0.35J1 and J c2 2 ≈ 0.66J1. PACS codes: 75.10.Jm Quantized spin models 75.45.+j Macroscopic quantum phenomena in magnetic systems 1