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Physical review. B, Condensed matter

Zero-temperature properties of the quantumXYmodel with anisotropy

Chris J. Hamer, J. Oitmaa, Zheng Weihong

Published May 1, 1991• 32 citations
Publisher

Abstract

The spin-1/2 XY model on a square lattice is studied via series expansions around the Ising limit, and spin-wave theory. Series are calculated for the ground-state energy, mass gap, magnetization, and magnetic susceptibilities. Extrapolating these series to the isotropic limit, we find extremely good agreement with the predictions of second-order spin-wave theory.

DOI
10.1103/physrevb.43.10789

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The spin-1/2 XY model on a square lattice is studied via series expansions around the Ising limit, and spin-wave theory. Series are calculated for the ground-state energy, mass gap, magnetization, and magnetic susceptibilities. Extrapolating these series to the isotropic limit, we find extremely good agreement with the predictions of second-order spin-wave theory.
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We present high-precision quantum Monte Carlo results for the S=12S=\frac{1}{2}S=21​ XY\mathrm{XY}XY model on a two-dimensional square lattice, in the ground state as well as at finite temperature. The energy, the spin stiffness, the magnetization, and the susceptibility are calculated and extrapolated to the thermodynamic limit. For the ground state, we test a variety of finite-size scaling predictions of effective Lagrangian theory and find good agreement and consistency between the finite-size corrections for different quantities. The low-temperature behavior of the susceptibility and the internal energy is also in good agreement with theoretical predictions.
The spin wave theory of Kondo and Yamaji is applied to the spin 1/2 XY model in one to three dimensions. In one dimension, the value of the gap Δ which appears in the spectrum of x -component spin remains finite up to 0 K, and no phase transition occurs. The value of the nearest neighbour correlation function is in good agreement with the exact values. In three dimensions, Δ vanishes at a finite temperature, and the second order phase transition occurs. In two dimensions, as T →0, Δ becomes very small for square lattice and tends to zero as exp (- T 0 / T ) for triangular lattice, which means the non-existence of the phase transition. The susceptibility, however, becomes anomalously large for low temperatures, and the extrapolation of Curie-Weiss law gives a “fictitious” transition temperature whose value agrees with those given by the high temperature expansion and the real space renormalization group theory.
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