arXiv:cond-mat/0606098

Squeezed number eigenstate of XYZ Heisenberg antiferromagnetics under an magnetic field

Bing-Hao Xie, Shuo Jin, Wei-Xian Yan

Published Jun 5, 2006• 0 citations

Abstract

By using an algebraic diagonalization method, the XYZ Heisenberg antiferromagnetics under an external magnetic field is studied in the framework of spin-wave theory. The energy eigenstates are shown to be squeezed number states and the energy eigenvalues are obtained in some cases. Some quantum properties of the energy eigenstates, and the connection of the model with the two-mode coupled harmonic oscillators are also discussed.

DOI: 10.48550/arxiv.cond-mat/0606098

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arXiv:cond-mat/0606098

Squeezed number eigenstate of XYZ Heisenberg antiferromagnetics under an magnetic field

Bing-Hao Xie, Shuo Jin, Wei-Xian Yan

Published Jun 5, 2006• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.cond-mat/0606098

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The

XYZ

antiferromagnetic model in linear spin-wave frame is shown explicitly to have an

su(1,2)

algebraic structure: the Hamiltonian can be written as a linear function of the

su(1,2)

algebra generators. Based on it, the energy eigenvalues are obtained by making use of the similar transformations, and the algebraic diagonalization method is investigated. Some numerical solutions are given, and the results indicate that only one group solution could be accepted in physics.

\Gamma(\mathbf q=0)

and at the magnetic ordering wavevectors

\pm[\mathbf Q= (4\pi/3,0)]

, the excitation spectra become gapless in the thermodynamic limit, due to the slow, logarithmic divergence of the structure factor. However, these longitudinal modes on two-dimensional models may be considered as quasi-gapped, as any finite-size effect or small anisotropy will induce a large energy gap, when compared with the counterpart of the transverse spin-wave excitations. We have also investigated the excited states of the quasi-one-dimensional quantum antiferromagnets on hexagonal lattices, including the longitudinal modes based on the magnon-density waves. A model Hamiltonian with a uniaxial single-ion anisotropy is first studied by a spin-wave theory based on the one-boson method; the ground state thus obtained is employed for the study of the longitudinal modes. The full energy spectra of both the transverse modes (i.e., magnons) and the longitudinal modes are obtained as functions of the nearest-neighbor coupling and the anisotropy constants. We have found two longitudinal modes due to the non-collinear nature of the triangular antiferromagnetic order, similar to that of the phenomenological field theory approach by Affleck. The excitation energy gaps due to the anisotropy and the energy gaps of the longitudinal modes without anisotropy are then investigated. We then compares our results for the longitudinal energy gaps at the magnetic wavevectors with the experimental results for several antiferromagnetic compounds with both integer and non-integer spin quantum numbers, and we find good agreements after the higher-order contributions are included in our calculations.