Exact solutions of generalized Hubbard Hamiltonian for diamond vacancies

TL;DR

This paper introduces a new formalism using a generalized Hubbard Hamiltonian to accurately calculate electronic states of diamond vacancies, capturing symmetry and spin properties without configuration interaction.

Contribution

The paper develops a novel atomic orbital-based Hubbard model that predicts electronic states of diamond vacancies with exact configuration contributions, bypassing traditional molecular methods.

Findings

Accurately predicts absorption lines of vacancies, including GR1 and ND1.

Locates the low-lying triplet state 113 meV above the ground state.

Provides detailed energy states for neutral and charged vacancies.

Abstract

A new formalism to calculate electronic states of vacancies in diamond has been developed using many-body techniques.This model is based on prevoius molecular models but does not use configuration interaction and molecular orbital techniques. A generalized Hubbard Hamiltonian which consists of all electron-electron interaction terms is calculated on the atomic orbital bases. Spatial symmetry $T_{d}$ and spin information of system are included in the form of Hamiltonian, so the eigenstates have automatically the correct spin and symmetry properties. Optimizing two key parameters of the model that justifies already reported semi-empirical values can predict accurate values of the famous absorption lines in neutral and charged vacancies i.e. $GR1$ and $ND1$. With these parameters the location of the low lying $^{3}T_{1}$ state is 113 mev above the ground state. In addition to these levels whole of the energy states of the system is predicted. Since the results are obtained without configuration interaction the model can gives the exact contribution of electronic configurations in the ground and excited states of the neutral and charged vacancies. The new results of the model for the ground and excited states of GR1 are reported.