Treatment of highly correlated systems

The vacancy in diamond, apparently the simplest of defects, has proven to be a most stern test for theoretical modelling. The reasons for this are various - the vacancy is a system with localised electrons which are highly correlated. In the neutral charge state we have shown it is also a Jahn-Teller system, with a strong relaxation lowering the energy by 0.36 eV. Many electron (multiplet) effects mean that is not possible to treat the ground state of the neutral vacancy using density functional theory. The negative charge state can however be treated correctly identifiying the ground state as 4A2symmetry. We have also performed one of the few implementations of the von Barth method to a condensed matter system obtaining the excitation energies of this system, and a remarkably accurate result of 3.3 eV for the 4A2 symmetry to 4T1 transistion (experimentally 3.15 eV).

[Fig 1: Defect states associated with the vacancy in diamond. ]

To investigate the ground state of the neutral system we have used the quantum Monte Carlo approach. The aim was to correctly identify the symmetry of the ground state wavefunction, a task that is not possible with standard density functional theory. We obtained the 1E state as the ground state, in agreement with experiment. The splittings of the various many electron states obtainable from the one electron-like t2 symmetry Kohn-Sham states was as great as 2 eV with the GR1 optical absorption band being predicted as 1.5eV (expt 1.67 eV).

This work is particularly interesting as it is a first demonstration that diffusion Monte Carlo calculations can be used to obtain excitation energies for defect centres in solids in which the electrons are highly correlated. In this sense it achieved far more than a modest improvement over the quantitative accuracy of DFT calculations (as had been previously demonstrated for this technique).