Yangian Symmetry and Quantum Inverse Scattering Method for the One-Dimensional Hubbard Model

TL;DR

This paper develops a quantum inverse scattering framework for the 1D Hubbard model at zero density, revealing a simplified R-matrix structure and Yangian symmetry, leading to new integrable operators.

Contribution

It introduces a new R-matrix and monodromy matrix limit for the Hubbard model, connecting it to Yangian symmetry and integrable operators.

Findings

Simplified R-matrix in the zero-density limit

Representation of Yangian symmetry via monodromy matrix

Infinite series of commuting Yangian invariant operators

Abstract

We develop the quantum inverse scattering method for the one-dimensional Hubbard model on the infinite interval at zero density. $R$-matrix and monodromy matrix are obtained as limits from their known counterparts on the finite interval. The $R$-matrix greatly simplifies in the considered limit. The new $R$-matrix contains a submatrix which turns into the rational $R$-matrix of the XXX-chain by an appropriate reparametrization. The corresponding submatrix of the monodromy matrix thus provides a representation of the Y(su(2)) Yangian. From its quantum determinant we obtain an infinite series of mutually commuting Yangian invariant operators which includes the Hamiltonian.