Random dispersion approximation for the Hubbard model

TL;DR

This paper applies the Random Dispersion Approximation to study the Mott-Hubbard transition in the Hubbard model, using exact diagonalization to analyze ground-state properties and transition characteristics.

Contribution

It introduces the RDA as a finite-chain approximation to the Hubbard model in infinite dimensions, providing insights into the nature of the Mott-Hubbard transition.

Findings

RDA results agree with perturbative limits

Transition appears continuous at $U_c \\approx W$

Possible coexistence region suggests a complex transition scenario

Abstract

We use the Random Dispersion Approximation (RDA) to study the Mott-Hubbard transition in the Hubbard model at half band filling. The RDA becomes exact for the Hubbard model in infinite dimensions. We implement the RDA on finite chains and employ the Lanczos exact diagonalization method in real space to calculate the ground-state energy, the average double occupancy, the charge gap, the momentum distribution, and the quasi-particle weight. We find a satisfactory agreement with perturbative results in the weak- and strong-coupling limits. A straightforward extrapolation of the RDA data for $L\leq 14$ lattice results in a continuous Mott-Hubbard transition at $U_{\rm c}\approx W$. We discuss the significance of a possible signature of a coexistence region between insulating and metallic ground states in the RDA that would correspond to the scenario of a discontinuous Mott-Hubbard transition as found in numerical investigations of the Dynamical Mean-Field Theory for the Hubbard model.