LOW-LYING DISORDERED STATES WHEN GROUND-STATE LONG-RANGE ORDER EXISTS - LARGE-AMPLITUDE SPIN-WAVES

Quantum magnets whose ground states show long-range order (LRO) are considered. The existence of disordered states, i.e., without LRO, with zero relative excitation energies, is shown for Heisenberg ferromagnets and argued for in the case of Heisenberg antiferromagnets, independent of dimensionality. The disordered states are wave packets of long-wavelength spiral-like states q. For finite systems these states exhibit disordered-type correlation-function decay and small relative excitation energy, quite similarly to the low-lying disordered states found recently by Liang, Doucot, and Anderson and given major significance vis à vis the resonating-valence-bond theory of superconductivity. Our results show that the existence of such states is not special to low-dimensional antiferromagnets. It is shown that at small wave vectors q the excitation energy of q is of order q2 for ferromagnets and for antiferromagnets. The seeming paradox for antiferromagnets, in light of the spin-wave frequencies being linear in q, is resolved, essentially through the observation that q corresponds to spin waves with large amplitudes that are independent of q. © 1990 The American Physical Society.