Quasiclassical Hamiltonians for large-spin systems
Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany
2 Condensed Matter Physics Group and Center for Nonlinear Studies, Theoretical Division, LANL, MS-B258, Los Alamos, NM 87545, USA
Revised: 24 September 1999
Published online: 15 March 2000
We extend and apply a previously developed method for a semiclassical treatment of a system with large spin S. A multisite Heisenberg Hamiltonian is transformed into an effective classical Hamilton function which can be treated by standard methods for classical systems. Quantum effects enter in form of multispin interactions in the Hamilton function. The latter is written in the form of an expansion in powers of J/(TS), where J is the coupling constant. Main ingredients of our method are spin coherent states and cumulants. Rules and diagrams are derived for computing cumulants of groups of operators entering the Hamiltonian. The theory is illustrated by calculating the quantum corrections to the free energy of a Heisenberg chain which were previously computed by a Wigner-Kirkwood expansion.
PACS: 05.30.-d – Quantum statistical mechanics / 75.10.Hk – Classical spin models / 75.10.Jm – Quantized spin models
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000