Hubbard physics in the symmetric half-filled periodic Anderson-Hubbard model

TL;DR

This paper investigates the potential for a metal-insulator transition in the symmetric half-filled periodic Anderson-Hubbard model using exact diagonalization and a variational method, focusing on the behavior of double occupancy.

Contribution

It compares two computational methods to analyze the model and reveals how double occupancy behaves, highlighting differences in predictions of a transition.

Findings

Double occupancy remains finite without on-site Coulomb interaction.

Exact diagonalization and variational methods agree for finite $U_f$.

Gutzwiller method predicts a Brinkman-Rice transition at a critical $U_d^c$.

Abstract

Two very different methods -- exact diagonalization on finite chains and a variational method -- are used to study the possibility of a metal-insulator transition in the symmetric half-filled periodic Anderson-Hubbard model. With this aim we calculate the density of doubly occupied $d$ sites as a function of various parameters. In the absence of on-site Coulomb interaction ($U_f$) between $f$ electrons, the two methods yield similar results. The double occupancy of $d$ levels remains always finite just as in the one-dimensional Hubbard model. Exact diagonalization on finite chains gives the same result for finite $U_f$, while the Gutzwiller method leads to a Brinkman-Rice transition at a critical value ($U_d^c$), which depends on $U_f$ and $V$.