Family of Affine Quantum Group Invariant Integrable Extensions of Hubbard Hamiltonian

TL;DR

This paper introduces a family of integrable spin chain Hamiltonians with affine quantum group symmetry, extending the Hubbard model and exhibiting superconducting ground states through eta-pairing.

Contribution

It constructs new integrable extensions of the Hubbard Hamiltonian with affine quantum group symmetry and analyzes their spectral and ground state properties.

Findings

Eigenvalues match traditional models but with enhanced degeneracy.

New integrable models exhibit superconducting ground states.

Representations involve tensor products of quantum group modules.

Abstract

We construct the family of spin chain Hamiltonians, which have affine quantum group symmetry. Their eigenvalues coincide with the eigenvalues of the usual spin chain Hamiltonians, but have the degeneracy of levels, corresponding to affine quantum group. The space of states of these spin chains is formed by the tensor product of fully reducible representations of quantum group. The fermionic representations of constructed spin chain Hamiltonians show that we have new extensions of Hubbard Hamiltonians. All of them are integrable and have affine quantum group symmetry. The exact ground state of a such type model is presented, exhibiting superconducting behavior via eta-pairing mechanism.