SO(4) Symmetry of the Transfer Matrix for the One-Dimensional Hubbard Model

TL;DR

This paper clarifies the SO(4) symmetry of the transfer matrix in the one-dimensional Hubbard model using the quantum inverse scattering method, demonstrating invariance through fermionic R-matrices and conserved currents.

Contribution

It provides a detailed fermionic R-matrix formulation and shows the explicit SO(4) invariance of the transfer matrix and conserved currents in the Hubbard model.

Findings

Transfer matrix is invariant under SO(4) rotation.

Fermionic R-matrix satisfies graded Yang-Baxter relation.

Higher conserved currents are SO(4) invariant in Clifford algebra form.

Abstract

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 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.