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Theoretical and Mathematical Physics

Two-magnon states in a one-dimensional non-Heisenberg ferromagnet of spins = 1 with interactions up to third neighbors

Sadulla Mamarazhabovich Tashpulatov

Published May 1, 1996• 3 citations
Publisher
DOI
10.1007/bf02071376

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We consider a two-magnon systems in an ν-dimensional isotropic non-Heisenberg ferromagnet with spin value S = 3/2 and nearest-neighbor interactions. Spectrum and bound states (BS) of the system for all values of full quasi-momentum Λ, and for arbitrary value of lattice dimensionality ν, and for all values of Hamiltonian parameters are investigated. We show that (i) for arbitrary ν ≥ 2 and for full quasi-momentum in the form Λ = (Λ1; Λ2; … ;Λν) = (Λ0;Λ0; …; Λ0) the change of energy spectrum of the system is similar to that observed in the case of ν = 1. In this case the operator [Formula: see text] with J + J1 - 23J2 ≠ 0 has only one additional BS. (ii) The energy z of this additional BS is degenerate ν - 1 times. (iii) If Λ ≠ (Λ0;Λ0;…;Λ0), we show the existence no more 2ν + 1 bound states in the system in ν-dimensional lattice.

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Two-dimensional frustrated Heisenberg model: Variational study

Д. В. Дмитриев, V. Ya. Krivnov, А. А. Овчинников

The stability of the ferromagnetic phase of the two-dimensional (2D) quantum spin-1/2 model with nearest-neighbor ferro- and next-nearest neighbor antiferromagnetic interactions is studied. It turns out that values of exchange integrals at which the ferromagnetic state becomes unstable with respect to a creation of one and two magnons are different. This difference shows that the classical approximation is inapplicable to the study of the transition from the ferromagnetic to the singlet state in contrast with 1D case. This problem is investigated using a variational function. It is based on the boson representation of spin operators which is different from the Holstein-Primakoff approximation. This allows us to obtain an accurate estimate of the transition point and to study the character of the phase transition.

arXiv:cond-mat/9911491•Physical review. B, Condensed matter•Feb 1, 1997•14 citations
We consider a two-magnon systems in an ν-dimensional isotropic non-Heisenberg ferromagnet with spin value S = 3/2 and nearest-neighbor interactions. Spectrum and bound states (BS) of the system for all values of full quasi-momentum Λ, and for arbitrary value of lattice dimensionality ν, and for all values of Hamiltonian parameters are investigated. We show that (i) for arbitrary ν ≥ 2 and for full quasi-momentum in the form Λ = (Λ1; Λ2; … ;Λν) = (Λ0;Λ0; …; Λ0) the change of energy spectrum of the system is similar to that observed in the case of ν = 1. In this case the operator [Formula: see text] with J + J1 - 23J2 ≠ 0 has only one additional BS. (ii) The energy z of this additional BS is degenerate ν - 1 times. (iii) If Λ ≠ (Λ0;Λ0;…;Λ0), we show the existence no more 2ν + 1 bound states in the system in ν-dimensional lattice.
The stability of the ferromagnetic phase of the two-dimensional (2D) quantum spin-1/2 model with nearest-neighbor ferro- and next-nearest neighbor antiferromagnetic interactions is studied. It turns out that values of exchange integrals at which the ferromagnetic state becomes unstable with respect to a creation of one and two magnons are different. This difference shows that the classical approximation is inapplicable to the study of the transition from the ferromagnetic to the singlet state in contrast with 1D case. This problem is investigated using a variational function. It is based on the boson representation of spin operators which is different from the Holstein-Primakoff approximation. This allows us to obtain an accurate estimate of the transition point and to study the character of the phase transition.