Abstract
Hidden local gauge invariance in completely integrable lattice models of fermions including a one-dimensional small-poralon model and the one-dimensional (1D) Hubbard model is discussed. We find that Abelian U (1) and U (1) ⊗ U (1) gauge transformations appear in a 1D small-poralon model and in the 1D Hubbard model respectively. In a 1D small-polaron model, the exact energy spectrum turns out to be gauge-invariant whereas the eigenvectors are explicitly gauge-dependent. We believe that the same result also holds for the 1D Hubbard model. Moreover, there is also a discrete symmetry associated to Z 2⊗Z 2. When this symmetry is broken, we immediately obtain another completely integrable system in both cases.
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