Homolumo Gap from Dynamical Energy Levels

TL;DR

This paper presents a dynamical matrix model illustrating how fermionic interactions induce a gap in energy levels, analyzing the gap formation across different coupling regimes with potential intermediate structures.

Contribution

It introduces a novel dynamical matrix model linking fermionic interactions to energy gap formation, including analysis of strong, weak, and intermediate coupling effects.

Findings

Fermionic interactions create a gap between occupied and unoccupied energy levels.

The model describes gap development in both strong and weak coupling regimes.

Intermediate coupling may lead to homolumo 'kinks' in the energy spectrum.

Abstract

We introduce a dynamical matrix model where the matrix $X$ is interpreted as a Hamiltonian representing interaction of a bosonic system with a single fermion. We show how a system of second-quantized fermions influences the ground state of the whole system by producing a gap between the highest occupied eigenvalue and the lowest unoccupied eigenvalue. We describe the development of the gap in both, strong and weak coupling regime, while for the intermediate coupling strength we expect formation of homolumo "kinks".