Abstract
We prove a Goldstone-type theorem for a wide class of lattice and continuum quantum systems, both for the ground state and at nonzero temperature. For the ground state (T=0) spontaneous breakdown of a continuous symmetry implies no energy gap. For nonzero temperature, spontaneous symmetry breakdown implies slow clustering (noL 1 clustering). The methods apply also to nonzero-temperature classical systems.
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Partial financial support by Fundação de Amparo à Pesquisa do Estado de São Paulo.
Partial financial support by CNPq.
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Landau, L., Perez, J.F. & Wreszinski, W.F. Energy gap, clustering, and the Goldstone theorem in statistical mechanics. J Stat Phys 26, 755–766 (1981). https://doi.org/10.1007/BF01010937
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DOI: https://doi.org/10.1007/BF01010937