Quantum fluctuations in quantum lattice-systems with continuous symmetry

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.

14 pages. To appear in J.Stat.Phys

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• New Exactly Solvable Model of Strongly Correlated Electrons Motivated by High T_c Superconductivity
• Symmetry Breaking and Finite Size Effects in Quantum Many-Body Systems
• Spin Excitations and Sum Rules in the Heisenberg Antiferromagnet
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