Quantum Breathing of an Impurity in a One-dimensional Bath of Interacting Bosons

TL;DR

This paper investigates the real-time dynamics of a single impurity in a one-dimensional interacting bosonic bath, revealing complex breathing modes and limitations of the Luttinger-liquid approximation.

Contribution

It demonstrates the application of TDMRG to study impurity breathing modes beyond traditional Luttinger-liquid theory in one-dimensional bosonic systems.

Findings

Impurity exhibits a well-defined breathing mode with specific frequency and damping.

Luttinger-liquid theory applies only in weak coupling regimes.

TDMRG captures dynamics beyond Luttinger-liquid predictions.

Abstract

By means of time-dependent density-matrix renormalization-group (TDMRG) we are able to follow the real-time dynamics of a single impurity embedded in a one-dimensional bath of interacting bosons. We focus on the impurity breathing mode, which is found to be well-described by a single oscillation frequency and a damping rate. If the impurity is very weakly coupled to the bath, a Luttinger-liquid description is valid and the impurity suffers an Abraham-Lorentz radiation-reaction friction. For a large portion of the explored parameter space, the TDMRG results fall well beyond the Luttinger-liquid paradigm.