SO(4) Symmetry of the Transfer Matrix for the One-Dimensional Hubbard Model
نویسندگان
چکیده
The SO(4) invariance of the transfer matrix for the one-dimensional Hubbard model is clarified from the QISM (quantum inverse scattering method) point of view. We demonstrate the SO(4) symmetry by means of the fermionic L-operator and the fermionic R-matrix, which satisfy the graded Yang-Baxter relation. The transformation law of the fermionic L-operator under the SO(4) rotation is identified with a kind of gauge transformation, which determines the corresponding transformation of the fermionic creation and annihilation operators under the SO(4) rotation. The transfer matrix is confirmed to be invariant under the SO(4) rotation, which ensures the SO(4) invariance of the conserved currents including the Hamiltonian. Furthermore, we show that the representation of the higher conserved currents in terms of the Clifford algebra gives manifestly SO(4) invariant forms. JSPS fellow e-mail: [email protected] e-mail: [email protected] e-mail: [email protected] §
منابع مشابه
Tunable Defect Mode in One-Dimensional Ternary Nanophotonic Crystal with Mirror Symmetry
In this paper, the properties of the defect mode in the photonic band gap ofone-dimensional ternary photonic crystals containing high temperature superconductorlayer (SPCs) have been theoretically investigated. We considered the quasi-periodiclayered structures by choosing two order of ternary Thue-Morse structures with mirrorsymmetry. We investigated the transmission spectra of these structure...
متن کاملThe Analytic Bethe Ansatz for a Chain with Centrally Extended su(2|2) Symmetry
We investigate the integrable structure of spin chain models with centrally extended su(2|2) and psu(2, 2|4) symmetry. These chains have their origin in the planar AdS/CFT correspondence, but they also contain the one-dimensional Hubbard model as a special case. We begin with an overview of the representation theory of centrally extended su(2|2). These results are applied in the construction an...
متن کاملThe su(n) Hubbard model
The one-dimensional Hubbard model is known to possess an extended su(2) symmetry and to be integrable. I introduce an integrable model with an extended su(n) symmetry. This model contains the usual su(2) Hubbard model and has a set of features that makes it the natural su(n) generalization of the Hubbard model. Complete integrability is shown by introducing the L-matrix and showing that the tra...
متن کاملScattering matrix and excitation spectrum of the Hubbard model.
We consider the one-dimensional Hubbard model at half filling. We show that both excitation spectrum and S-matrix are determined by the SO(4) symmetry of the model. The complete set of excitations is given by the scattering states four elementary excitations, which form the fundamental representation of SO(4). We evaluate the exact S-matrix, which satisfies the Yang-Baxter relation. The results...
متن کاملSU ( 2 ) × SU ( 2 ) - invariant Scattering Matrix of the Hubbard Model
We consider the one-dimensional half-filled Hubbard model. We show that the excitation spectrum is given by the scattering states of four elementary excitations, which form the fundamental representation of SU(2)×SU(2). We determine the exact two-particle Scattering matrix, which a solution of the Yang-Baxter equation and reflects the SO(4) symmetry of the model. The results for repulsive and a...
متن کامل