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

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...

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Bibliographic Details
Published in:Journal of mathematical physics 1990-06, Vol.31 (6), p.1544-1550
Main Authors: Zhou, Huan‐Qiang, Jiang, Lin‐Jie, Wu, Ping‐Feng
Format: Article
Language:English
Subjects:
Classical and quantum physics: mechanics and fields
Classical mechanics of discrete systems: general mathematical aspects
Exact sciences and technology
Physics
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Summary: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 Z 2⊗Z 2. Once this symmetry is broken, one immediately obtains another nontrivial solution to the Yang–Baxter relations. UFaipxr
ISSN:0022-2488
1089-7658
DOI:10.1063/1.529023