A hidden symmetry in an excited state of the one-dimensional Hubbard model

Huan-Qiang Zhou, Lin-Jie Jiang, Ping‐Feng Wu

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

G. Uimin, С. В. Фомичев

А. А. Овчинников

P B Ramos, Marcio Jose Martins

We formulate in terms of the quantum inverse scattering method the algebraic Bethe ansatz solution of the one-dimensional Hubbard model. The method developed is based on new set of commutating relations which encodes a hidden symmetry of 6-vertex type.

Cornelius F. Coll

C. M. Villet, W.‐H. Steeb

The spectrum of the half-filled four point Hubbard model with cyclic boundary conditions is calculated in Wannier and Bloch representation. The total number operator and total spin operator are conserved and spin-reversal symmetry exists. In Wannier representation we have additionally the C 4 v symmetry and in Bloch representation we have the total momentum operator wich is conserved. After group-theoretical reduction with respect to these symmetries, it is found that degeneracy still exists in some subspaces. From the theorem of von Neumann and Wigner we conjecture that there is a hidden symmetry. Since there is a Lax representation for the one-dimensional Hubbard model we conjecture that the hidden symmetry can be found from the Lax pair.