A study of cooperative breathing-mode in molecular chains

TL;DR

This paper develops a non-perturbative model for cooperative breathing modes in 1D molecular chains, revealing a novel quantum phase transition from a Luttinger liquid to a charge-density wave state at strong electron-phonon coupling.

Contribution

It introduces a new effective model that captures cooperative breathing modes with dominant next-nearest-neighbor hopping and enhanced nearest-neighbor repulsion, highlighting a unique phase transition not seen in similar models.

Findings

Identifies a second-order quantum phase transition at strong coupling.

Shows the transition involves a shift from Luttinger liquid to charge-density wave.

Demonstrates superextensive divergence in fidelity susceptibility.

Abstract

Using a controlled analytic non-perturbative treatment, that accounts for the quantum nature of the phonons, we derive a model that generically describes cooperative breathing-mode at strong electron-phonon interaction in one-band one-dimensional systems. The effective model involves a {\em next-nearest-neighbor} hopping (that dominates over the nearest-neighbor hopping at strong coupling) and a nearest-neighbor repulsion that is significantly enhanced due to incompatibility of neighboring dilations/compressions. At non-half filling, upon tuning the electron-phonon coupling, the system undergoes a period-doubling second-order quantum phase transition from a Luttinger liquid to a {\em conducting commensurate} charge-density-wave state: a phenomenon absent in both the Holstein model and the t-V model. Using fidelity to study the nature of the quantum phase transition, we find that the fidelity susceptibility shows a superextensive power law divergence as well as a remarkable scaling behavior: both together establish a second-order transition.