Heavy Particle in a d-dimensional Fermionic Bath: A Strong Coupling Approach

TL;DR

This paper studies the low temperature dynamics of a heavy particle in a fermionic environment, revealing dimension-dependent behaviors and employing a strong coupling approach to understand quasiparticle properties.

Contribution

It introduces a strong coupling method that exactly captures the orthogonality catastrophe and analyzes the quasiparticle weight across different dimensions.

Findings

Finite quasiparticle weight in two and higher dimensions

Algebraic decay of the propagator in one dimension

Valid saddle point approximation for large mass M

Abstract

We investigate the low temperature behavior of a heavy particle (mass $M$) in a fermionic bath. An effective action is considered which exactly implements the orthogonality catastrophe. It is equivalent to a model of local bosons coupling via a long-range interaction to the particle. The saddlepoint solution for the heavy particle propagator yields a finite quasiparticle weight in two and higher dimensions. In one dimension the propagator decays algebraically for long times. The saddle point approximation is valid for large $M$.