Volume 73, Number 2, January 2006
|Page(s)||278 - 284|
|Section||Condensed matter: electronic structure, electrical, magnetic, and optical properties|
|Published online||16 December 2005|
Flux expulsion and greedy bosons: Frustrated magnets at large
Department of Physics and Astronomy, Johns Hopkins University Baltimore, MD, USA
2 Laboratoire de Physique Théorique de l'Ecole Normale Supérieure CNRS-UMR8549 - Paris, France
3 Department of Physics, Princeton University - Princeton, NJ, USA
Accepted: 25 November 2005
We investigate the mean-field theory for frustrated quantum magnets. First, we establish some general properties of its solutions; in particular, for small spin we propose simple rules for determining the saddle points of optimal energy. We then apply these insights to the pyrochlore lattice. For spins on a single tetrahedron, we demonstrate a continuous ground-state degeneracy for any value of the spin length. For the full pyrochlore lattice, this degeneracy translates to a large number of near-degenerate potential saddle points. Remarkably, it is impossible to construct a saddle point with the full symmetry of the Hamiltonian —at large N, the pyrochlore magnet cannot be a spin liquid. Nonetheless, for realistic finite values of N, tunnelling between the nearly degenerate saddle points could restore the full symmetry of the Hamiltonian.
PACS: 75.10.Jm – Quantized spin models / 75.10.-b – General theory and models of magnetic ordering / 71.27.+a – Strongly correlated electron systems; heavy fermions
© EDP Sciences, 2006
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