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Generalized Coherent States and the Continuous Heisenberg XYZ Model With One-Ion Anisotropy
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In this paper, the authors formulate the reduction procedure of the quantum lattice Heisenberg XYZ model to the continuum Landau-Lifshitz model based on generalized coherent states (GCS) of the SU(2) group.Abstract:
On the basis of the method of generalized coherent states (GCS) of the SU(2) group we formulate the reduction procedure of the quantum lattice Heisenberg XYZ model to the continuum Landau-Lifshitz model. The choice of the GCS representation is determined (i) by their proximity to the corresponding classical states and (ii) by similarity of the geometric structure of the homogeneous spaces on which the SU(2) GCS and the vector of the magnetic moment of the corresponding Landau-Lifshitz model are defined. The present reduction procedure is allowed only in the case of weak anisotropy. Accounting for a weak one-ion anisotropy leads to the Landau-Lifshitz model with a renormalized anisotropy tensor. The contribution of such an anisotropy vanishes for the s = 1/2 case.read more
Citations
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Integrable (2+1)-Dimensional Spin Models with Self-Consistent Potentials
TL;DR: This paper identifies three different integrable spin systems in (2 + 1) dimensions by introducing the interaction of the spin field with more than one scalar potential, or vector potential,, or both, and deduces the equivalent nonlinear Schrodinger family of equations.
Journal ArticleDOI
Integrable (2 + 1)-Dimensional Spin Models with Self-Consistent Potentials
TL;DR: In this paper, the Schrodinger-Hirota-Maxwell-Bloch equations were derived in (2 + 1) dimensions by introducing the interaction of the spin field with more than one scalar potential or vector potential, or both.
Journal ArticleDOI
Darboux transformation and exact solutions of the integrable Heisenberg ferromagnetic equation with self-consistent potentials
Z. S. Yersultanova,M. Zhassybayeva,Kuralay Yesmakhanova,Gulgasyl Nugmanova,Ratbay Myrzakulov +4 more
TL;DR: In this paper, the Darboux transformation of the M-XCIX equation is constructed using the DT and a 1-soliton solution of the XCIX is presented.
Journal ArticleDOI
The classical limit for the Holstein-Primakoff representation in the soliton theory of Heisenberg chains
TL;DR: In this article, the Holstein-Primakoff boson representation of the anisotropic Heisenberg chain was studied in the classical limit by means of the complete series.
Journal ArticleDOI
Integrable geometric flows of interacting curves/surfaces, multilayer spin systems and the vector nonlinear Schrödinger equation
TL;DR: In this article, the integrable multilayer spin systems, namely, the multi-layer M-LIII equation, were studied and their relation with the geometric flows of interacting curves and surfaces in some geometric flows was investigated.
References
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Book
Progress in Low Temperature Physics
TL;DR: In this article, the specific heat of high-T c superconductors was studied. But the authors focused on the scaling of 3 He-4 He mixtures and did not consider the properties of the order parameter collective modes of these mixtures.
Journal ArticleDOI
Experiments on simple magnetic model systems
L.J. de Jongh,A.R. Miedema +1 more
TL;DR: In this article, a review of the theoretical and experimental results obtained on simple magnetic model systems on magnetic lattices of dimensionality 1, 2, and 3 is presented, with particular attention paid to the approximation of these model systems in real crystals, viz how they can be realized or be expected to exist in nature.
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Solitons in molecular systems
TL;DR: Agarwal as discussed by the authors pointed out that the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches, but also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related.
Journal ArticleDOI
Dynamics of classical solitons (in non-integrable systems)
TL;DR: A survey of the properties of soliton-type solutions to non-linear wave equations appearing in various fields of physics is given in this paper, where the results of computer experiments on the dynamics of the formation and interaction (in one-space-dimensional geometry) of solit-type objects are presented at length.
Journal ArticleDOI
Non-linear effects in quasi-one-dimensional models of condensed matter theory
V.G. Makhankov,V.K. Fedyanin +1 more
TL;DR: A survey of non-linear (soliton-like) effects in certain models of condensed matter theory is given in this paper, where the corresponding nonlinear evolution equations are obtained and examined with due respect for the existence of localized finite energy solutions.