Local density of states of the interacting resonant level model at zero temperature

TL;DR

This paper investigates the zero-temperature local density of states in the interacting resonant level model, revealing how increasing interactions alter the spectral resonance and introduce new finite-energy peaks, supported by numerical and analytical methods.

Contribution

It provides new insights into the spectral properties of the interacting resonant level model, including the emergence of finite-energy peaks and a novel second exponent in the spectral function.

Findings

Resonance peak at zero energy disappears with increased interaction.

Two new finite-energy peaks emerge as interactions grow.

The spectral function height and width scale differently, defining a second exponent.

Abstract

We present results of the impurity local density of states of the interacting resonant level model at zero temperature. We concentrate on low-energy properties and predominantly use the numerical renormalisation group technique. As interaction is increased, we find that the resonance peak at zero energy disappears, while two new peaks at finite energy emerge. This is in the absence of any field breaking the resonance. We further show that the height of the spectral function does not scale in the same way as the width, and in fact defines a second distinct exponent. We back up our results with analytic strong-coupling calculations as well as an analytic diagrammatic renormalisation group calculation that rather surprisingly gets the second exponent exactly, even for strong interactions.