Fermionic R-Operator and Integrability of the One-Dimensional Hubbard Model

Abstract

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.

25 pages

References in corpus (3)

• The Quantum Inverse Scattering Method for Hubbard-like Models
• Fermionic R-Operator for the Fermion Chain Model
• SO(4) Symmetry of the Transfer Matrix for the One-Dimensional Hubbard Model

Cited by in corpus (24)

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• Results on the symmetries of integrable fermionic models on chains
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• Hubbard-Shastry lattice models
• On the theory of plateau-plateau transitions in Quantum Hall Effect
• Network Models: Action formulation
• The Tetrahedron Zamolodchikov Algebra and the AdS5 x S5 S-matrix
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• Fermionic R-Operator and Algebraic Structure of 1D Hubbard Model: Its application to quantum transfer matrix
• Solutions of the Yang-Baxter equation: descendants of the six-vertex model from the Drinfeld doubles of dihedral group algebras
• A variational approach for the Quantum Inverse Scattering Method
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• Integrable chain models with staggered R-matrices
• 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
• The Yang-Baxter paradox