New integrable 1D models of superconductivity

TL;DR

This paper introduces new integrable one-dimensional lattice models of electrons with su(2)xsu(2) symmetry, classifies known and novel models, and explores their integrability and diagonalization challenges.

Contribution

It classifies all nearest-neighbour integrable models with su(2)xsu(2) symmetry and identifies new models including integrable Hubbard generalizations.

Findings

12 R-matrices of difference form identified

Some models relate to known models like XXX spin chain

Most new models cannot be diagonalized with standard Bethe Ansatz

Abstract

In this paper we find new integrable one-dimensional lattice models of electrons. We classify all such nearest-neighbour integrable models with su(2)xsu(2) symmetry following the procedure first introduced in arXiv:1904.12005. We find 12 R-matrices of difference form, some of which can be related to known models such as the XXX spin chain and the free Hubbard model, and some are new models. In addition, integrable generalizations of the Hubbard model are found by keeping the kinetic term of the Hamiltonian and adding all terms which preserve fermion number. We find that most of the new models can not be diagonalized using the standard nested Bethe Ansatz.