Absence of Renormalization of the Specific Heat Coefficient of the Interacting Fermion Systems

TL;DR

This paper demonstrates that in Fermi liquid systems, the specific heat coefficient remains unrenormalized by the wave-function renormalization factor, challenging longstanding beliefs.

Contribution

It provides a theoretical proof that the specific heat coefficient is not affected by wave-function renormalization in Fermi liquids.

Findings

The specific heat coefficient $b3$ is not renormalized by $Z$ in Fermi liquids.

Challenges the traditional view of renormalization effects on thermodynamic quantities.

Supports the stability of Fermi liquid theory in describing interacting fermion systems.

Abstract

Contrary to the longtime and widely conceived belief, we proved that the specific heat coefficient $\gamma$ --also called Sommerfeld coefficient -- of the interacting Fermion system is not renormalized by the wave-function renormalization factor $Z$ as far as the system remains a Fermi liquid state.