Approximate scaling relation for the anharmonic electron-phonon problem

TL;DR

This paper derives an approximate scaling relation for the transition temperature to charge-density-wave instability in anharmonic electron-phonon systems, applicable across various interaction strengths and phonon frequencies, including non-Fermi liquids.

Contribution

It introduces a universal scaling relation using wave-function renormalization, extending applicability to non-Fermi liquid systems in electron-phonon interactions.

Findings

The scaling relation accurately predicts transition temperatures across diverse parameters.

It demonstrates validity even in non-Fermi liquid regimes.

Provides a unified framework for understanding charge-density-wave instabilities.

Abstract

An approximate scaling relation is found for the transition temperature to a charge-density-wave instability in the anharmonic electron-phonon problem, which maps a wide range of interaction strengths, anharmonicities, and phonon frequencies onto a common functional form. The relation employs the wave-function renormalization parameter and is valid even for systems that are not Fermi liquids.