Application of the coherent state representation in the theory of magnetism: I. The heisenberg model

Kenneth H. Douglass

Tadeusz Lulek

Vladmir G. Makhankov, R. Myrzakulov, Алексей Владимирович Маханьков

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.

Narasimhaiengar Mukunda, Arvind, S. Chaturvedi +1 more

We consider the problem of existence of the diagonal representation for operators in the space of a family of generalized coherent states associated with a unitary irreducible representation of a (compact) Lie group. We show that necessary and sufficient conditions for the possibility of such a representation can be obtained by combining Clebsch–Gordan theory and the reciprocity theorem associated with induced unitary group representations. Applications to several examples involving SU(2), SU(3), and the Heisenberg–Weyl group are presented, showing that there are simple examples of generalized coherent states which do not meet these conditions. Our results are relevant for phase–space description of quantum mechanics and quantum state reconstruction problems.

Eugene Stanley

M. J. Škrinjaŕ, D. Kapor, S. D. Stojanović

Soliton excitations in the anisotropic Heisenberg chain are studied in the classical limit by means of the Holstein-Primakoff boson representation, taking into account the complete series. The results obtained are equivalent to those obtained by the classical treatment of spins. The connection with different calculations using limited numbers of terms is established, as well as the relation to the generalised coherent-states method.