Flux expulsion and greedy bosons: Frustrated magnets at large

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

Abstract

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.