Hidden local gauge invariance in the one-dimensional Hubbard model and its equivalent coupled spin model

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Hidden local gauge invariance in the one-dimensional (1-D) Hubbard model and its equivalent coupled spin model is studied. It is found that Abelian U(1)⊗U(1) gauge transformations appear in both cases. Furthermore, it is shown that the energy spectrum is gauge invariant whereas the eigenvectors are explicitly gauge dependent. However, this result relies heavily on Shastry’s conjecture about the eigenvalue of the transfer matrix for the 1-D Hubbard model. Lastly, there is also a discrete symmetry associated to Z2⊗Z2. Once this symmetry is broken, one immediately obtains another nontrivial solution to the Yang–Baxter relations. UFaipxr