Local Classical and Quantum Criticality due to Electron-Vibration Interaction

TL;DR

This paper investigates the local classical and quantum critical behavior arising from electron-vibration interactions, revealing a transition from quantum to classical regimes influenced by temperature and dissipation, with potential experimental relevance in carbon nanotubes.

Contribution

It provides a detailed analysis of the critical properties of the Yu-Anderson model, highlighting the crossover between quantum and classical criticality and the effects of dissipation.

Findings

Identification of the energy scale separating quantum and classical criticality

Demonstration of the impact of dissipation on correlation functions

Prediction of observable phenomena in carbon nanotubes with defects

Abstract

We study the local classical and quantum critical properties of electron-vibration interaction, represented by the Yu-Anderson model. It exhibits an instability, similar to the Wentzel-Bardeen singularity, whose nature resembles to weakly first order quantum phase transitions at low temperatures, and crosses over to Gaussian behaviour with increasing temperature. We determine the dominant energy scale separating the quantum from classical criticality, study the effect of dissipation and analyze its impact on correlation functions. Similar phenomenon should be observable in carbon nanotubes around local defects.