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Le Journal de Physique Colloques

MONTE CARLO STUDY OF QUANTUM SPIN SYSTEMS ON THE SQUARE LATTICE

Yutaka Okabe, Macoto Kikuchi

Published Dec 1, 1988• 1 citation
Publisher

Abstract

The quantum XXZ model of spin 1/2 on the square lattice is numerically investigated. We use both the conventional quantum Monte Carlo method and the projector Monte Carlo method. The ground-state energy and the existence of the long-range order are examined.
DOI
10.1051/jphyscol:19888639

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The existence of long-range order is proved under certain conditions for the antiferromagnetic XYZ model on the simple cubic or the square lattice. In particular, the spin-1/2 XXZ model on the square lattice is shown to have ground-state long-range order if the exchange anisotropy Δ satisfies 0≦ Δ <0.20 or Δ >1.72, which improves the result of Kubo and Kishi. The existence of long-range order of the z -component of the spin operator is proved for the XXZ model with XY -like anisotropy (0≦ Δ ≦1) under certain conditions. A similar result is shown to hold for the long-range order in the x -direction for the Ising-like model ( Δ ≧1). The XXZ model on the two-dimensional hexagonal lattice is proved to have finite ground-state long-range order for any value of Δ (≧0) if S ≧1 and for Δ >2.55 when S =1/2.
We employ the determinant projector quantum Monte Carlo method to investigate the ground-state magnetic properties in the Mott insulating states of the half-filled SU(4)SU(4)SU(4) and SU(6)SU(6)SU(6) Fermi-Hubbard model in the two-dimensional square lattice, which is free of the sign problem. The long-range antiferromagnetic Neel order is found for the SU(4)SU(4)SU(4) case with a small residual Neel moment. Quantum fluctuations are even stronger in the SU(6)SU(6)SU(6) case. Numeric results are consistent with either a vanishing or even weaker Neel ordering than that of SU(4)SU(4)SU(4).