Renormalization group method based on the ionization energy theory

TL;DR

This paper demonstrates that the ionization energy theory (IET) is a renormalized framework consistent with established renormalization group formalisms, enabling derivation of physical properties like heat capacity based on ionization energy.

Contribution

It establishes IET as a renormalized theory compatible with known formalisms and applies it to derive material properties related to ionization energy.

Findings

IET satisfies Gell-Mann-Low, Shankar, and Zinn-Justin renormalization formalisms.

The electron-electron and electron-phonon interactions in IET are mathematically equivalent.

Heat capacity and Debye frequency can be derived as functions of ionization energy.

Abstract

Proofs are developed to explicitly show that the ionization energy theory (IET) is a renormalized theory, which mathematically exactly satisfies the renormalization group formalisms developed by Gell-Mann-Low, Shankar and Zinn-Justin. However, the cutoff parameter for IET relies on the energy-level spacing, instead of lattice spacing in \textbf{k}-space. Subsequently, we apply the earlier proofs to prove that the mathematical structure of the ionization-energy dressed electron-electron screened Coulomb potential is exactly the same as the ionization-energy dressed electron-phonon interaction potential. The latter proof is proven by means of the second-order time-independent perturbation theory with the heavier effective mass condition, as required by the electron-electron screened Coulomb potential. The outcome of this proof is that we can derive the heat capacity and the Debye frequency as a function of ionization energy, which can be applied in strongly correlated matter and nanostructures.