FermionicR-Operator and Algebraic Structure of 1D Hubbard Model: Its Application to Quantum Transfer Matrix

Abstract

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 which is a local operator acting on fermion Fock spaces. In particular, S O (4) symmetry and the invariance under the partial particle-hole transformation are shown. Second, a genuinely fermionic quantum transfer matrix (QTM) can be constructed in terms of the fermionic R -operator. By use of the algebraic Bethe ansatz, the fermionic QTM is diagonalized and its properties are discussed.