Electron self-trapping at quantum and classical critical points

TL;DR

This paper investigates electron self-trapping phenomena near quantum and classical critical points using path integral methods, revealing the formation of localized states called fluctuons and analyzing their properties across different regimes.

Contribution

It introduces the concept of quantum and classical fluctuons, providing a detailed analysis of their characteristics and the conditions for their formation near critical points.

Findings

Quantum fluctuon energy relates to the true energy spectrum boundary.

Classical fluctuon energy is a saddle-point in the density of states tail.

Singular perturbation theory emerges in some interaction regimes.

Abstract

Using Feynman path integral technique estimations of the ground state energy have been found for a conduction electron interacting with order parameter fluctuations near quantum critical points. In some cases only \textit{singular} perturbation theory in the coupling constant emerges for the electron ground state energy. It is shown that an autolocalized state (quantum fluctuon) can be formed and its characteristics have been calculated depending on critical exponents for both weak and strong coupling regimes. The concept of fluctuon is considered also for the classical critical point (at finite temperatures) and the difference between quantum and classical cases has been investigated. It is shown that, whereas the quantum fluctuon energy is connected with a true boundary of the energy spectrum, for classical fluctuon it is just a saddle-point solution for the chemical potential in the exponential density of states fluctuation tail.