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Flux expulsion and greedy bosons: Frustrated magnets at large N

2005; Institute of Physics; Volume: 73; Issue: 2 Linguagem: Inglês

10.1209/epl/i2005-10389-2

1286-4854

Oleg Tchernyshyov, Roderich Moessner, S. L. Sondhi,

Quantum many-body systems

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 largeN, 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.