QUANTUM FLUCTUATIONS IN QUANTUM-LATTICE SYSTEMS WITH CONTINUOUS SYMMETRY

We discuss conditions for the absence of spontaneous breakdown of cont inuous symmetries in quantum lattice systems at T = 0. Our analysis is based on Pitaevskii and Stringari's idea that the uncertainty relatio n can be employed to show quantum fluctuations. For one-dimensional sy stems, it is shown that the ground state is invariant under a continuo us transformation if a certain uniform susceptibility is finite. For t he two- and three-dimensional systems, it is shown that truncated corr elation functions cannot decay any more rapidly than \r\(-d+1) wheneve r the continuous symmetry is spontaneously broken. Both of these pheno mena occur owing to quantum fluctuations. Our theorems cover a wide cl ass of quantum lattice systems having not-too-long-range interactions.