Europhys. Lett.
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
Europhys. Lett., 73 (2), pp. 278-284 (2006)
DOI: 10.1209/epl/i2005-10389-2

Flux expulsion and greedy bosons: Frustrated magnets at large $\mth{N}$

O. Tchernyshyov1, R. Moessner2 and S. L. Sondhi3

1  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

received 10 October 2005; accepted 25 November 2005
published online 16 December 2005

We investigate the Sp(N) 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.

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.

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