# Random dispersion approximation for the Hubbard model - Condensed Matter > Strongly Correlated Electrons

Abstract: We use the Random Dispersion Approximation RDA to study the Mott-Hubbardtransition in the Hubbard model at half band filling. The RDA becomes exact forthe Hubbard model in infinite dimensions. We implement the RDA on finite chainsand employ the Lanczos exact diagonalization method in real space to calculatethe ground-state energy, the average double occupancy, the charge gap, themomentum distribution, and the quasi-particle weight. We find a satisfactoryagreement with perturbative results in the weak- and strong-coupling limits. Astraightforward extrapolation of the RDA data for $L\leq 14$ lattice results ina continuous Mott-Hubbard transition at $U { m c}\approx W$. We discuss thesignificance of a possible signature of a coexistence region between insulatingand metallic ground states in the RDA that would correspond to the scenario ofa discontinuous Mott-Hubbard transition as found in numerical investigations ofthe Dynamical Mean-Field Theory for the Hubbard model.

Author: S. Ejima, F. Gebhard, R.M. Noack

Source: https://arxiv.org/