Strong-Correlations Versus U-Center Pairing and Fractional Aharonov-Bohm Effect

The influence of the interaction between electrons on the Aharonov-Bohm effect is investigated in the framework of the Hubbard model. The repulsion between electrons associated with strong correlation is compared with the case of attraction such as $U$-center pairing. The most interesting case, when two electrons are located on a ring, is investigated in detail using the Bethe ansatz method and by exact numerical diagonalization of the Hubbard hamiltonian. It is shown that the quasi half quantum flux periodicity occurs for any nonzero values of $U$. For large number of sites, or strong U, the quasi periodicity becomes an exact half quantum flux periodicity. However the character of the state created on the ring is different in both cases. In the case of $U$-center pairing the electrons are bound in pairs located on the same site. For strong correlations(large positive $U$) the electrons tend to be far from each other as possible. We show by numerical solution of Bethe ansaz equations that for three electrons the flux periodicity of the ground state energy is equal to 1/3. The one third periodicity may occur even for small values of the ratio $U/t$, for the very dilute system. It is shown analytically using the Bethe ansaz equations for $N$ electrons, that for dilute systems with arbitrary value of the Hubbard repulsion $U$,