On the link between SO(4) invariance and Bethe states of the 1D Hubbard model

Mario Salerno

Fabian H.L. Eβler, V. E. Korepin, Kareljan Schoutens

Chen Ning Yang

Pedro S. Goldbaum

Yukiko Umeno

The algebraic structure of the 1D Hubbard model is studied by means of the fermionic R-operator approach. This approach treats the fermion models directly in the framework of the quantum inverse scattering method. Compared with the graded approach, this approach has several advantages. First, the global properties of the Hamiltonian are naturally reflected in the algebraic properties of the fermionic R-operator. We want to note that this operator is a local operator acting on fermion Fock spaces. In particular, SO(4) symmetry and the invariance under the partial particle hole transformation are discussed. Second, we can construct a genuinely fermionic quantum transfer transfer matrix (QTM) in terms of the fermionic R-operator. Using the algebraic Bethe Ansatz for the Hubbard model, we diagonalize the fermionic QTM and discuss its properties.

Mario Salerno

We show how to construct SO(4) invariant functions for strongly correlated Fermi systems on lattices of finite sizes. We illustrate the method on the case of the 1D Hubbard chain with four and with six sites.