Numerical Studies of the Combined Effects of Interactions and Disorder at Metal-Insulator Transitions
MetadataShow full item record
We first study noninteracting electrons moving on corner-sharing tetrahedral lattices, which represent the conduction path of LiAlyTi2−yO4. A uniform box distribution type of disorder for the on-site energies is assumed. Using the Dyson-Mehta Delta-3 statistics as a criterion for localization, we have determined the critical disorder (Wc/t = 14.5 ± 0.25) and the mobility-edge trajectories. Then we study the Anderson-Hubbard model, which includes both interactions and disorder, using a real-space self-consistent Hartree-Fock theory. We provide a partial assessment on how the Hartree-Fock theory approximates the ground states of the Anderson-Hubbard model, using small clusters which can be solved exactly. The Hartree-Fock theory works very well in reproducing the ground-state energies and local charge densities. However, it does not work as well in representing the spin-spin correlations. To find the ground state, one needs to allow maximum degree of freedom in spins. Evidence of screening of disorder by the interactions is provided. We have applied the Hartree-Fock theory to large-scale three-dimensional simple cubic lattices. For a disorder strength of W/t = 6, weak interactions (U/t ≤ 3) enhance the density of states at the Fermi level and the low-frequency conductivity. There are no local magnetic moments, and the AC conductivity is Drude-like. With stronger interactions (U/t ≥ 4), the density of states at the Fermi level and the low-frequency conductivity are both suppressed. These are accompanied by the presence of local magnetic moments, and the conductivity becomes non-Drude-like. A metal-to-insulator transition is likely to take place at a critical Uc/t ≈ 8 – 9. We find that (i) the formation of magnetic moments is essential to the suppression of the density of states at the Fermi level, and therefore essential to the metal-insulator transition; (ii) the form of magnetic moments does not matter; and (iii) these results do not depend on the type of lattice or the type of disorder.