Estimates of Effective Hubbard Model Parameters for C20 isomers

TL;DR

This paper develops an effective Hubbard model for C20 isomers using quantum Monte Carlo and exact diagonalization, fitting parameters to DFT and experimental data to study electronic correlations and spectral properties.

Contribution

It introduces a method to estimate Hubbard model parameters for C20 isomers by combining DFT calculations with quantum Monte Carlo and exact diagonalization techniques.

Findings

Estimated hopping parameter t for C20 isomers

Calculated U/t ratios indicating strong correlations

Predicted spectral peak shifts and energy gaps

Abstract

We report on an effective Hubbard Hamiltonian approach for the study of electronic correlations in C$_{20}$ isomers, cage, bowl and ring, with quantum Monte Carlo and exact diagonalization methods. The tight-binding hopping parameter, $t$, in the effective Hamiltonian is determined by a fit to density functional theory calculations, and the on-site Coulomb interaction, $U/t$, is determined by calculating the isomers' affinity energies, which are compared to experimental values. For the C$_{20}$ fullerene cage we estimate $t_{\rm cage}\simeq 0.68-1.36$ eV and $(U/t)_{\rm cage} \simeq 7.1-12.2$. The resulting effective Hamiltonian is then used to study the shift of spectral peaks in the density of states of neutral and one-electron-doped C$_{20}$ isomers. Energy gaps are also extracted for possible future comparison with experiments.