Exact solution of the one-dimensional Hubbard model in a magnetic field

By means of the Bethe-ansatz method, the one-dimensional Hubbard model with repulsive on-site coupling in an external magnetic field is solved exactly. It is found that the energy of the ground state depends on the magnetic flux φ through the ring formed by a periodic lattice chain, and the lowest-energy state corresponds to φ=n(hc/2e), with n an integer and -e the electron charge. The calculations illustrate that the strongly correlated Hubbard ring with periodic boundary conditions in its ground state is a superconducting ring. It can also be shown that the system possesses an internal SU(2)xSU(2) symmetry