Extended Hubbard model on a C$_{20}$ molecule

TL;DR

This study investigates the electronic correlations and magnetic properties of a C20 molecule using an extended Hubbard model, revealing how Coulomb interactions influence pair-binding, spin states, and correlation functions.

Contribution

It provides the first detailed analysis of the effects of nearest neighbor Coulomb interaction V on pairing and magnetic properties of C20 within an extended Hubbard framework.

Findings

Non-zero V suppresses pair-binding in doped C20.

Transitions between spin singlet and triplet states occur with varying U or V.

Short-range spin and charge correlations are observed, with weak pairing enhancement at molecular scale.

Abstract

The electronic correlations on a C$_{20}$ molecule, as described by an extended Hubbard Hamiltonian with a nearest neighbor Coulomb interaction of strength $V$, are studied using quantum Monte Carlo and exact diagonalization methods. For electron doped C$_{20}$, it is known that pair-binding arising from a purely electronic mechanism is absent within the standard Hubbard model (V=0). Here we show that this is also the case for hole doping for $0<U/t\leq 3$ and that, for both electron and hole doping, the effect of a non-zero $V$ is to work against pair-binding. We also study the magnetic properties of the neutral molecule, and find transitions between spin singlet and triplet ground states for either fixed $U$ or $V$ values. In addition, spin, charge and pairing correlation functions on C$_{20}$ are computed. The spin-spin and charge-charge correlations are very short-range, although a weak enhancement in the pairing correlation is observed for a distance equal to the molecular diameter.