Ground state of one-dimensional fermion-phonon systems

TL;DR

This paper introduces a new reflection positivity framework to analyze one-dimensional fermion-phonon systems, demonstrating the presence of charge-density-wave order and long-range order in the ground state.

Contribution

It develops a novel reflection positivity approach based on operator inequalities for studying ground states of fermion-phonon systems.

Findings

Reflection positivity describes charge-density-wave order.

Long-range Coulomb interactions lead to CDW long-range order.

Ground state exhibits stable CDW order under certain conditions.

Abstract

A new framework for the reflection positivity, based on order-preserving operator inequalities, is proposed. This framework is utilized to investigate one-dimensional fermion-phonon systems, with a particular focus on the detailed examination of ground state properties. Our analysis reveals that the reflection positivity provides a consistent description of the charge-density-wave (CDW) order in such systems. Additionally, we establish the existence of CDW long-range order in the ground state when the Coulomb interaction is long range.