Quantum Deformations of the One-Dimensional Hubbard Model

TL;DR

This paper explores the quantum deformation of the one-dimensional Hubbard model's algebraic structure, deriving a new R-matrix and Hamiltonian with three parameters, advancing understanding of integrable quantum systems.

Contribution

It introduces a quantum-deformed algebraic framework for the Hubbard model, deriving a new R-matrix and Hamiltonian with three parameters, and relates it to existing models.

Findings

Derived the fundamental R-matrix for the quantum-deformed algebra.

Constructed an integrable spin chain Hamiltonian with three parameters.

Connected the new Hamiltonian to the two-parametric Hamiltonian by Alcaraz and Bariev.

Abstract

The centrally extended superalgebra psu(2|2)xR^3 was shown to play an important role for the integrable structures of the one-dimensional Hubbard model and of the planar AdS/CFT correspondence. Here we consider its quantum deformation U_q(psu(2|2)xR^3) and derive the fundamental R-matrix. From the latter we deduce an integrable spin chain Hamiltonian with three independent parameters and the corresponding Bethe equations to describe the spectrum on periodic chains. We relate our Hamiltonian to a two-parametric Hamiltonian proposed by Alcaraz and Bariev which can be considered a quantum deformation of the one-dimensional Hubbard model.