Tsutomu Momoi
Quantum fluctuations in quantum lattice-systems with continuous symmetry
(47K, LaTeX)
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 one-dimensional
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 three-dimensional 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 lattice-systems having
not-too-long-range interactions.