Fermionic R-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. 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.

22 pages, no figures

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Cited by in corpus (6)

• Free Fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT
• Correlation length of the 1D Hubbard Model at half-filling : equal-time one-particle Green's function
• The Lax pair for the fermionic Bazhanov-Stroganov $R$-operator
• The tetrahedral Zamolodchikov algebra for the fermionic Bazhanov-Stroganov R-operator
• On extension of the Yang-Baxter equation and the fermionic $R$-operator
• On integrability of the one-dimensional Hubbard model