Anomalous Oscillations due to Aharonov–Bohm and Aharonov–Casher Effects of the One-Dimensional Hubbard Ring in the Strong Coupling Limit

Abstract

We investigate anomalous oscillations due to the Aharonov–Bohm (AB) and Aharonov–Casher (AC) effects of the one-dimensional Hubbard ring with flux in the strong coupling limit. By using the exact diagonalization method and the Shiba transformation, we examine the energies of the ground-state and a few excited states in the presence of the flux producing the AB or AC effect, where the transformation not only reverses the sign of the interaction U but also exchanges the role between the AB and AC effects in the model Hamiltonian. We systematically classify the AB and AC oscillations by using the number of minima Nmin of the ground-state energy as a function of a normalized phase shift ϕ for 0 ≤ ϕ < 1, and clarify the close relationship between the AB and AC effects. For example, it is shown that Nmin is given by NL − Ne (NL − N↑ + N↓) for the AB (AC) effect in the very strong attraction, where NL, Ne, N↑, and N↓ are the system size, the total number of electrons, the number of electrons with up-spin, and th...