Exact solution of the Hubbard model with boundary hoppings and fields

The Hubbard model with boundary hopping integrals and fields is proposed and solved exactly by means of the Bethe ansatz method. We find that for certain values of the boundary hopping integrals and fields the ground state contains boundary bound states, these new types of states are represented as “boundary charge and spin strings”. We show that the boundary bound states are realized at a strong boundary interaction for large values of the boundary hopping integrals or the boundary fields. The magnetic moment and charge of the boundary have been calculated numerically as a function of the magnetic field and band filling. It is found that the “boundary charge strings” solutions define the properties of the boundary.