SYMMETRIES OF THE HUBBARD MODEL AND THE θ TERM IN THE σ-MODEL

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Abstract
Recently, it has been shown that the strong coupling limit of the half-filled Hubbard model has SU(2) gauge invariance. The 2+1-dimensional nonlinear a model with the customary θ term does not have this symmetry — instead it has a U(1) gauge symmetry. A modification of the θ term is suggested so that the model acquires SU(2) — or rather SO(3) —gauge symmetry. The symmetries of this modified model thus resemble more closely those of the strongly coupled half-filled Hubbard model. Gauge invariance of the new model, unlike that of the U(1) model, requires quantization of the angle θ. The allowed θ values are mπ/2 ( mod 2π) with m an integer. Hence the allowed soliton spins are m/4 (m∈Z) while their statistics are governed by their spins in the usual way.

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