Homolumo Gap and Matrix Model

TL;DR

This paper introduces a dynamical matrix model linking random matrix theory to quantum systems, demonstrating how fermionic interactions create an energy gap in the system's spectrum.

Contribution

It presents a novel matrix model that connects Gaussian ensembles with fermionic interactions affecting spectral properties.

Findings

Fermionic interactions induce a gap in the eigenvalue spectrum.

The matrix M acts as a Hamiltonian for a boson-fermion system.

The model relates random matrix theory to quantum many-body physics.

Abstract

We discuss a dynamical matrix model by which probability distribution is associated with Gaussian ensembles from random matrix theory. We interpret the matrix M as a Hamiltonian representing interaction of a bosonic system with a single fermion. We show that 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.