The quantum vs classical aspects of one dimensional electron-phonon systems revisited by the renormalization group method

TL;DR

This paper uses an extended renormalization group method to analyze quantum and classical properties of Peierls states in one-dimensional electron-phonon systems, revealing quantum corrections and transition nature at various phonon frequencies.

Contribution

It introduces an extended RG approach that accounts for retardation effects, providing new insights into quantum corrections and transition behaviors in 1D electron-phonon models.

Findings

Quantum corrections to the Peierls gap are quantified at arbitrary phonon frequencies.

The nature of quantum-classical transitions is clarified in weak coupling regimes.

The method applies to models with spinless and spin-1/2 fermions interacting with phonons.

Abstract

An extension of the renormalization group method that includes the effect of retardation for the interactions of a fermion gas is used to re-examine the quantum and classical properties of Peierls- like states in one dimension. For models of spinless and spin-1/2 fermions interacting with either intra or intermolecular phonons the quantum corrections to the Peierls gap at half-filling are determined at arbitrary phonon frequency. The nature of quantum-classical transitions is clarified in weak coupling.