TY - JOUR

T1 - Flux expulsion and greedy bosons

T2 - Frustrated magnets at large N

AU - Tchernyshyov, O.

AU - Moessner, R.

AU - Sondhi, Shivaji Lal

PY - 2006/1/15

Y1 - 2006/1/15

N2 - 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.

AB - 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.

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U2 - 10.1209/epl/i2005-10389-2

DO - 10.1209/epl/i2005-10389-2

M3 - Article

AN - SCOPUS:30844435515

SN - 0295-5075

VL - 73

SP - 278

EP - 284

JO - EPL

JF - EPL

IS - 2

ER -