Dirac Impurity in a Luttinger liquid

TL;DR

This paper investigates how a quantum impurity interacts with a 1D superfluid described by Luttinger liquid theory, revealing two distinct dynamical regimes and potential experimental implications.

Contribution

It introduces a linked cluster expansion approach to analyze impurity dynamics in a Luttinger liquid, identifying quasiparticle and orthogonality catastrophe regimes.

Findings

Identification of quasiparticle regime with finite impurity lifetime

Discovery of infrared-dominated regime with orthogonality catastrophe

Potential experimental signatures in cold atom systems

Abstract

We consider a linearly-dispersing quantum impurity interacting through a contact density-density term with a one-dimensional (1D) superfluid described by the Tomonaga-Luttinger liquid theory. Using a linked cluster expansion we characterize the impurity dynamics by calculating approximate expressions for the single-particle Green's function and for the time evolution of the density profile. We show the existence of two different dynamical regimes: (i) a $\textit{quasiparticle}$ regime, dominated by the presence of a finite lifetime for the host impurity, and (ii) an $\textit{infrared-dominated}$ regime, where the impurity causes a Anderson's orthogonality catastrophe of the 1D bath. We discuss the possible experimental consequences of these findings for cold atoms experiments.