ASP Online Seminars: Exact Kohn-Sham Density Functional Theory on a Lattice
We formulate a set of equations that facilitate an exact numerical solution of the Kohn-Sham potential for a finite Hubbard chain with nearest neighbour hopping and arbitrary site potentials. The approach relies on a mapping of the non-interacting Kohn-Sham ground state wave function onto the exact interacting system wave function and two interconnected self-consistent cycles. The self-consistent cycles are performed within the framework of the Kohn-Sham non-interacting system without any direct reference to the interacting system. The first self-consistent cycle updates the mapping of the non-interacting wavefunction onto the interacting wavefunction based on a trial input density, while the second self-consistent cycle updates the Kohn-Sham potential to yield the trial density. At the solution point, our algorithm yields the exact Kohn-Sham potential, the correlation energy, and the ground-state energy of the interacting system.
This talk will be followed by a short presentation of an initiative in mathematics called Maths Camp. In this second part of my talk, I will explain what is a maths camp, its objectives, and how to get involved.
Keywords: Density Functional Theory; Hubbard Model; Lattice DFT; Maths Camp