Quantum Phase Transitions in an Ionic Hubbard Model in One Dimension

We study quantum phase transitions in an ionic Hubbard model in one dimension. This model accounts for electrons in alternating potentials with a lattice period of 2. For a specified alternating potential of strength $\Delta$, we change the local repulsion between spin-up and spin-down electrons, $U$, for the model to exhibit a quantum phase transition from a band insulator to a Mott insulator. Via exact diagonalization with a modified Lanczos method, we find that, as we tune $U$, the ground-state energy shows a level crossing at half-filling. We obtain a phase diagram of the model by using a finite-size scaling method. Also, we find an interesting feature of double occupancy around the phase transitions.