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Communications in Theoretical Physics

The q -Deformed SU(2) Quantum Antiferromagnetic Model

Zhong‐Yi Lu, Yan Hong

Published Apr 1, 1993• 0 citations
Publisher

Abstract

In this paper we set up a q -analogous Holstein-Primakoff transformation (HPT) and obtain the q -deformed spin-wave solutions. We apply a mean-field treatment that is arranged to preserve some nonlinearity of the Hamiltonian, and the results turn out to be interesting, e.g., a gapful spectrum of the elementary excitation spectrum is found, which is different from the spin-wave results for the conventionial model, and the specific heat is therefore modified greatly. The properties of the Néel state and the ground state are investigated.

DOI
10.1088/0253-6102/19/3/303

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In this paper we set up a q -analogous Holstein-Primakoff transformation (HPT) and obtain the q -deformed spin-wave solutions. We apply a mean-field treatment that is arranged to preserve some nonlinearity of the Hamiltonian, and the results turn out to be interesting, e.g., a gapful spectrum of the elementary excitation spectrum is found, which is different from the spin-wave results for the conventionial model, and the specific heat is therefore modified greatly. The properties of the Néel state and the ground state are investigated.
A q -deformed SU(2) Heisenberg (3-dimensional) spin model is set up, and the q -deformed spin-wave solution is obtained through the q -analogous Holstein-Primakoff transformation. The result is given for small γ = ln q , which is the quantity characterizing the nonlinearity of the Hamiltonian. A mean-field treatment is arranged to preserve (at least some of) the nonlinearity, and the ordinary ferromagnet ground state is shown as the exact ground state of the new system. Interesting results are obtained for this nonlinear model:(i) There is an energy gap between the ground state and the first excited one, thus the ground state is stable under small perturbation of the background; (ii) the specific heat per volume is modified by a small term proportional to the (1/2)-th power of temperature and the square of γ , which is qualitatively different from the conventional model, and (iii) the magnetization M(T) is modified by a factor that depends on γ .
Using the q analog of the Holstein-Primakoff boson realization of the su(2) generators, we show that a type of q-deformed binomial state that corresponds to the Heine distribution can be identified as an su(2)q{)}_{\mathit{q}})q​ coherent state. This fact is a q extension of the fact that the ordinary binomial state is a particular su(2) coherent state when the Holstein-Primakoff transformation is employed.
In terms of spinless fermions and spin waves, we describe magnetic properties of a spin-1/2 ferromagnetic– antiferromagnetic bond-alternating chain which behaves as a Haldane-gap antiferromagnet. On one hand, we employ the Jordan–Wigner transformation and treat the fermionic Hamiltonian within the Hartree–Fock approximation. On the other hand, we employ the Holstein– Primakoff transformation and modify the conventional spin-wave theory so as to restore the sublattice symmetry. We calculate the excitation gap, the specific heat, the magnetic susceptibility, magnetization curves, and the nuclear spin-lattice relaxation rate with varying bond alternation. These schemes are further applied to a bond-alternating tetramerized chain which behaves as a ferrimagnet. The fermionic language is particularly stressed as a useful tool to investigate one-dimensional spin-gapped antiferromagnets, while the bosonic one works better for ferrimagnets.
We introduce a quantum antiferromagnet model, having exactly soluble thermodynamic properties. It is an infinite range antiferromagnetic Ising model put in a transverse field. The free energy gives the ground state energy in the zero temperature limit and it also gives the low temperature behaviour of the specific heat, the exponential variation of which gives the precise gap magnitude in the excitation spectrum of the system. The detailed behaviour of the (random sublattice) staggard magnetisation and susceptibilities are obtained and studied near the Néel temperature and the zero temperature quantum critical point.
In terms of spinless fermions and spin waves, we describe the magnetic properties of a spin-1/2 ferromagnetic-antiferromagnetic bond-alternating chain which behaves as a Haldane-gap antiferromagnet. On the one hand, we employ the Jordan–Wigner transformation and treat the fermionic Hamiltonian within the Hartree–Fock approximation. On the other hand, we employ the Holstein–Primakoff transformation and modify the conventional spin-wave theory so as to restore the sublattice symmetry. We calculate the excitation gap, the specific heat, the magnetic susceptibility, magnetization curves, and the nuclear spin-lattice relaxation rate with varying bond alternation. These schemes are further applied to a bond-alternating tetramerized chain which behaves as a ferrimagnet. The fermionic language is particularly stressed as a useful tool for investigating one-dimensional spin-gapped antiferromagnets, while the bosonic one works better for ferrimagnets.
Thermodynamics of the qqq-deformed Kittel--Shore model for spin-1 particles
Quantum algebras (qqq-algebras) have been used in the literature to deform spin-chain models. In particular, in previous works by the present authors, the Kittel--Shore Hamiltonian was deformed using suq(2)\mathfrak{su}_q(2)suq​(2) algebra. The deformed Hamiltonian was presented for a general spin, and the thermodynamic properties were studied for spin-1/2 particles. In this paper, we focus on the qqq-deformation of the Kittel--Shore model for spin-1 systems. We analyse the impact of this deformation on the thermodynamic properties and phase transitions of the system as a function of the deformation parameter qqq. Specifically, we study the specific heat, magnetic susceptibility, and magnetisation, including a detailed analysis of the Curie temperature characterising the ferromagnetic phase. Furthermore, a finite-size scaling analysis is conducted for both the ferromagnetic and antiferromagnetic cases. Results are systematically compared with those of the undeformed model to reveal the physical effects of the qqq-deformation.