Flux expulsion and greedy bosons: frustrated magnets at large N

TL;DR

This paper explores the properties of frustrated quantum magnets using Sp(N) mean-field theory, revealing large degeneracies and symmetry-breaking behaviors in pyrochlore lattices at large N, with implications for spin liquid states.

Contribution

It introduces simple rules for saddle point determination in Sp(N) theory and analyzes degeneracies and symmetry properties in pyrochlore lattices at large N.

Findings

Ground state degeneracy on a single tetrahedron.

Large number of near-degenerate saddle points in pyrochlore lattice.

Full symmetry of the Hamiltonian cannot be realized at large N.

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.