Quantum fluctuations in geometrically frustrated antiferromagnet

Many geometrically frustrated antiferromagnets have thermodynamically degenerate classical ground states. I investigate the effects of quantum fluctuations as a driving force of symmetry breaking, for the Heisenberg model on the pyrochlore lattice at zero temperature. In the semiclassical limit, I find that a collinear spin order minimizes the zero-point energy and is most stabilized among q = 0 orders. In the quantum limit, a two-stage symmetry breaking in the spin-singlet sector is predicted, and the system is separate into two intertwining parts. One part shows a triple-q order of dimers, with a large stabilization energy and gapful excitations. The other part shows a uniform order of either dimers or tetramers, with a substantially reduced energy scale and gapless excitations. The presence of multiple energy scales is a manifestation of geometrical frustration. (C) 2002 Elsevier Science Ltd. All rights reserved.