KAGOME-LATTICE AND TRIANGULAR-LATTICE HEISENBERG ANTIFERROMAGNETS - ORDERING FROM QUANTUM FLUCTUATIONS AND QUANTUM-DISORDERED GROUND-STATES WITH UNCONFINED BOSONIC SPINONS

The kagome-lattice quantum Heisenberg antiferromagnet is studied by a large-N expansion based upon groups with symplectic Sp(N) symmetry. Two distinct types of ground states are found. (i) For large values of the "spin" the ground state has long-range magnetic order with the spins ordered in a square-root 3 x square-root 3 structure with 9 sites per unit cell. Quantum fluctuations are explicitly shown to select this structure from the large number of classically degenerate states. The only zero-energy excitations about the magnetically ordered state are shown to be the physical, infinite-wavelength, Goldstone spin waves; in contrast the naive semiclassical theory has zero-energy spin waves at all wave vectors. (ii) For small values of the "spin," the ordered moment disappears and we obtain a quantum-disordered ground state with no broken symmetries. As in previous work on frustrated square-lattice antiferromagnets, this state is argued to possess unconfined, spin-1/2, bosonic, spinon excitations for all values of the underlying lattice spin. A similar, small-"spin" quantum-disordered ground state with unconfined bosonic spinons is studied in the triangular-lattice quantum Heisenberg antiferromagnet by extending earlier results. A large N, Sp(N) theory of the classical kagome Heisenberg antiferromagnet at finite temperature is also presented: fluctuations of the square-root 3 x square-root 3 structure dominate, with a correlation length which diverges exponentially in the zero-temperature limit. The significance of these results for experimental kagome-lattice systems is discussed.