A goldstone mode in the Kawasaki-Ising model |
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Authors: | Claudio Albanese |
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Affiliation: | (1) Institute for Advanced Study, School of Mathematics, 08540 Princeton, New Jersey;(2) Present address: Department of Mathematics, University of Toronto, 3359 Mississagua Road North, L5L 1C6 Mississagua, Ontario, Canada |
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Abstract: | The hydrodynamic regime of superfluids is dominated by a Goldstone mode corresponding to a spontaneously brokenU(1) symmetry. In this article we map the Kawasaki-Ising model for a classical lattice gas into a quantum model for a superfluid and establish a connection between the normal density fluctuations of the first and the Goldstone mode of the second. The fact that the quantum model we obtain describes a superfluid derives from an inequality by Penrose and Onsager which gives a lower bound to the Bose-Einstein condensate density. Mathematically, the Goldstone mode can be described by means of a quantum extension of the local algebra of the Ising model. The classification of its irreducible representations requires an additionalU(1) phase factor and the correspondingU(1) gauge symmetry is spontaneously broken for all finite values of the temperature and of the density. |
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Keywords: | Ising model Monte Carlo dynamics spontaneous gauge symmetry breaking |
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