Abstract
We discuss conditions for the absence of spontaneous breakdown of continuous symmetries in quantum lattice systems atT=0. Our analysis is based on Pitaevskii and Stringari's idea that the uncertainty relation can be employed to show quantum fluctuations. For one-dimensional systems, it is shown that the ground state is invariant under a 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.
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Momoi, T. Quantum fluctuations in quantum lattice systems with continuous symmetry. J Stat Phys 85, 193–210 (1996). https://doi.org/10.1007/BF02175562
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DOI: https://doi.org/10.1007/BF02175562