 96126 Tsutomu Momoi
 Quantum fluctuations in quantum latticesystems with continuous symmetry
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Apr 11, 96

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Abstract. We discuss conditions for the absence of spontaneous breakdown of
continuous symmetries in quantum lattice systems at $T=0$. Our analysis
is based on Pitaevskii and Stringari's idea that the uncertainty relation
can be employed to show quantum fluctuations. For the onedimensional
systems, it is shown that the ground state is invariant under the continuous
transformation if a certain uniform susceptibility is finite.
For the two and threedimensional systems, it is shown that truncated
correlation functions cannot decay any more rapidly than $r^{d+1}$
whenever the continuous symmetry is spontaneously broken.
Both of these phenomena occur owing to quantum fluctuations.
Our theorems cover a wide class of quantum latticesystems having
nottoolongrange interactions.
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