Algebraic Solution of the Hubbard Model on the Infinite Interval

TL;DR

This paper develops an algebraic method using quantum inverse scattering to diagonalize the one-dimensional Hubbard model on an infinite line, classifying eigenstates and analyzing symmetries.

Contribution

It introduces an algebraic diagonalization approach for the Hubbard model on the infinite line, including classification of eigenstates and symmetry analysis with Yangian quantum groups.

Findings

Eigenstates classified as scattering, bound pairs, and bound states.

Derived creation and annihilation operators and calculated the S-matrix.

Identified Yangian symmetry and its role in state transformations.

Abstract

We develop the quantum inverse scattering method for the one-dimensional Hubbard model on the infinite line at zero density. This enables us to diagonalize the Hamiltonian algebraically. The eigenstates can be classified as scattering states of particles, bound pairs of particles and bound states of pairs. We obtain the corresponding creation and annihilation operators and calculate the S-matrix. The Hamiltonian on the infinite line is invariant under the Yangian quantum group Y(su(2)). We show that the n-particle scattering states transform like n-fold tensor products of fundamental representations of Y(su(2)) and that the bound states are Yangian singlet.