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.
The XXZ Heisenberg spin chain is considered. Following results are obtained: for the Bosonization of the spin Hamiltonians widely used Holstein-Primakoff transformations are very sensitive to the way of breaking an initial system symmetry by the ground state. In the case of easy-axis models only such transformations may be applied without previous analysis (at any rate when an external magnetic field vanishes). Others are subjected to the corresponding symmetry analysis.Es wird die XXZ-Heisenbergspinkette betrachtet. Folgende Ergebnissc werden erhalten: die fur die Bosonisation des Spin-Hamiltonoperators weit genxtzten Holstein-Primakoff-Transformationen sind sehr empfindlich gegenuber der Art, wie die urspriingliche Systemsymmetrie durch den Grundzustand gebrochen wird. Im Falle des Modells leichter Achsen konnen nur solche Transformationen ohne vorherige Analyse (fur eine beliebige Rate, wenn ein 5uBeres Magnetfeld verschwindet) angewendet werden. Andere sind einer entsprechenden Symmetrieanalyse unterworfen.
Generalized Coherent States (GCS) are constructed (and discussed) in order to study quasiclassical behaviour of quantum spin models of the Heisenberg type. Several such models are taken to their semiclassical limits, whose form depends on the spin value as well as the Hamiltonian symmetry. In the continuum approximation, SU(2)/U(1) GCS when applied give rise to the well-known Landau-Lifshitz classical phenomenology. For arbitrary spin values one obtains a lattice of coupled nonlinear oscillators. Corresponding classical continuum models are described as well.
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