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arXiv:0804.1171

The Spin-1 Heisenberg Antiferromagnet: New Results from Series Expansions

J. Oitmaa, Chris J. Hamer

Published Apr 8, 2008• 0 citations
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Abstract

We calculate ground state properties (energy, magnetization, susceptibility) and one-particle spectra for the $S = 1$ Heisenberg antiferromagnet with easy-axis or easy-plane single site anisotropy, on the square lattice. Series expansions are used, in each of three phases of the system, to obtain systematic and accurate results. The location of the quantum phase transition in the easy-plane sector is determined. The results are compared with spin-wave theory.

DOI
10.48550/arxiv.0804.1171

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We calculate ground state properties (energy, magnetization, susceptibility) and one-particle spectra for the S=1S = 1S=1 Heisenberg antiferromagnet with easy-axis or easy-plane single site anisotropy, on the square lattice. Series expansions are used, in each of three phases of the system, to obtain systematic and accurate results. The location of the quantum phase transition in the easy-plane sector is determined. The results are compared with spin-wave theory.
We calculate ground state properties (energy, magnetization, susceptibility) and one-particle spectra for the S=1S=1S=1 Heisenberg antiferromagnet with easy-axis or easy-plane single-site anisotropy on the square lattice. Series expansions are used, in each of three phases of the system, to obtain systematic and accurate results. The location of the quantum phase transition in the easy-plane sector is determined. The results are compared to spin-wave theory.
We develop series expansions for the ground state properties of the Hubbard model by introducing an Ising anisotropy into the Hamiltonian. For the two-dimensional square lattice half-filled Hubbard model, the ground state energy, local moment, sublattice magnetization, uniform magnetic susceptibility, and spin stiffness are calculated as a function of U/t, where U is the Coulomb constant and t is the hopping parameter. Magnetic susceptibility data indicate a crossover around U\ensuremath{\approxeq}4 between spin density wave antiferromagnetism and Heisenberg antiferromagnetism. Comparisons with Monte Carlo simulations, random phase approximation result, and mean-field solutions are also made.
Using the coupled cluster method for high orders of approximation and complementary exact diagonalization studies we investigate the ground state properties of the spin-1/2 J1−−J2{J}_{1}--{J}_{2}J1​−−J2​ frustrated Heisenberg antiferromagnet on the square lattice. We have calculated the ground state energy, the magnetic order parameter, the spin stiffness, and several generalized susceptibilities to probe magnetically disordered quantum valence-bond phases. We have found that the quantum critical points for both the N\'eel and collinear orders are ${J}_{2}^{c1}\ensuremath{\approx}(0.44\ifmmode\pm\else\textpm\fi{}0.01){J}_{1}$ and ${J}_{2}^{c2}\ensuremath{\approx}(0.59\ifmmode\pm\else\textpm\fi{}0.01){J}_{1}$, respectively, which are in good agreement with the results obtained by other approximations. In contrast to the recent study by [Sirker et al. Phys. Rev. B 73, 184420 (2006)], our data do not provide evidence for the transition from the N\'eel to the valence-bond solid state to be first order. Moreover, our results are in favor of the deconfinement scenario for that phase transition. We also discuss the nature of the magnetically disordered quantum phase.
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
In this paper we have applied the coupled-cluster method to investigate the ground state of the spin-1 Heisenberg antiferromagnet with anisotropic exchange interaction and easy-plane single-ion anisotropy. A coupled-cluster approximation up to the second level has been performed to evaluate the ground-state energy and staggered magnetization for various lattices such as linear chain, honeycomb, square, simple cubic, and body-centered-cubic lattice. The convergence of our results is fairly rapid, and thus the coupled-cluster method seems to be a practical tool for calculating ground-state energy of a spin system since only the first few levels of approximation will be needed in actual practice.
The Green's-function Monte Carlo (GFMC) method is used to calculate very accurate ground-state energies of the two-dimensional, spin-1/2 Heisenberg antiferromagnet. The computations are performed on L\ifmmode\times\else\texttimes\fi{}L square lattices up to L=16 with varying uniform magnetization, which allows the extraction of the perpendicular susceptibility (\ensuremath{\chi}) and spin-wave velocity (c). These two quantities are the lattice- or cutoff-dependent parameters that allow one to map the long-wavelength properties of the antiferromagnet onto the nonlinear \ensuremath{\sigma} model and so are of general interest. Systematic errors present in previous GFMC calculations are addressed and corrected to yield results in excellent agreement with other numerical methods. I find, for the ground-state energy per site, -0.669 34(3); the susceptibility renormalization factor, ${\mathit{Z}}_{\mathrm{\ensuremath{\chi}}}$=0.535(5); and the spin-wave velocity renormalization factor, Zc{\mathit{Z}}_{\mathit{c}}Zc​=1.10(3). Finite-size effects in the extraction of Zc{\mathit{Z}}_{\mathit{c}}Zc​ and ${\mathit{Z}}_{\mathrm{\ensuremath{\chi}}}$ are discussed. The value of ${\mathit{Z}}_{\mathrm{\ensuremath{\chi}}}$ computed here is in agreement with the series-expansion results of Singh and of Zheng, Oitmaa, and Hamer, thereby clearing up a previous inconsistency between the series-expansion and quantum Monte Carlo predictions.