### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 278-284 |

Number of pages | 7 |

Journal | Europhysics Letters |

Volume | 73 |

Issue number | 2 |

DOIs | |

State | Published - Jan 15 2006 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

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## Cite this

*Europhysics Letters*,

*73*(2), 278-284. https://doi.org/10.1209/epl/i2005-10389-2