The 1D Hubbard Model

Adolfo Avella, F. Mancini, Marı́a del Mar Sánchez-López

有希子 梅野, Masahiro Shiroishi, Miki Wadati

We propose a new type of the Yang-Baxter equation (YBE) and the decorated Yang-Baxter equation (DYBE). Those relations for the fermionic R-operator were introduced recently as a tool to treat the integrability of the fermion models. Using the YBE and the DYBE for the XX fermion model, we construct the fermionic R-operator for the one-dimensional (1D) Hubbard model. It gives another proof of the integrability of the 1D Hubbard model. Furthermore a new approach to the SO(4) symmetry of the 1D Hubbard model is discussed.

Yupeng Wang, Wen‐Li Yang, Junpeng Cao +1 more

Ruihong Yue, Tetsuo Deguchi

We have found the eigenvalues of the transfer matrices for the 1D Hubbard model and for the coupled XY model with a twisted boundary condition by using the analytic Bethe ansatz method. Under a particular condition the two models have the same Bethe ansatz equations. We have also proved that the periodic 1D Hubbard model is exactly equal to the coupled XY model with a non-trivial twisted boundary condition at the level of Hamiltonians and transfer matrices.

V. E. Korepin, Fabian H. L. Eßler