Exact exchange-correlation potential of a ionic Hubbard model with a free surface

TL;DR

This study computes the exact exchange-correlation potential of a lattice Hubbard model with a free surface, verifying key density functional theory concepts and revealing how correlations influence surface potentials and energy gaps.

Contribution

It provides the first exact lattice calculation of the xc-potential for a Hubbard chain with a surface, confirming continuum DFT results and elucidating correlation effects on surface barriers and gaps.

Findings

The fundamental gap equals the Kohn-Sham gap plus the xc-potential jump.

In the ionic regime, the xc-contribution to the gap equals V.

In the Mott regime, the xc-contribution is determined by U.

Abstract

We use Lanczos exact diagonalization to compute the exact exchange-correlation (xc) potential of a Hubbard chain with large binding energy ("the bulk") followed by a chain with zero binding energy ("the vacuum"). Several results of density functional theory in the continuum (sometimes controversial) are verified in the lattice. In particular we show explicitly that the fundamental gap is given by the gap in the Kohn-Sham spectrum plus a contribution due to the jump of the xc-potential when a particle is added. The presence of a staggered potential and a nearest-neighbor interaction V allows to simulate a ionic solid. We show that in the ionic regime in the small hopping amplitude limit the xc-contribution to the gap equals V, while in the Mott regime it is determined by the Hubbard U interaction. In addition we show that correlations generates a new potential barrier at the surface.