Exact equilibrium results in the Interacting Resonant Level Model

TL;DR

This paper derives exact analytical expressions for the susceptibility and energy scale in the interacting resonant level model, validated by numerical simulations, and explores the limitations of Bethe ansatz methods.

Contribution

It provides the first exact analytical results for the susceptibility and energy scale in the equilibrium interacting resonant level model, combining bosonization and integrability techniques.

Findings

Analytical expression for the energy scale $T_K$ with excellent numerical agreement.

Bethe ansatz requires parameter renormalization to match numerical results.

Results extend to multiple leads with some open questions remaining.

Abstract

We present exact results for the susceptibility of the interacting resonant level model in equilibrium. Detailed simulations using both the Numerical Renormalization Group and Density Matrix Renormalization Group were performed in order to compare with closed analytical expressions. By first bosonizing the model and then utilizing the integrability of the resulting boundary sine-Gordon model, one finds an analytic expression for the relevant energy scale $T_K$ with excellent agreement to the numerical results. On the other hand, direct application of the Bethe ansatz of the interacting resonant level model does not correctly reproduce $T_K$ - however if the bare parameters in the model are renormalised, then quantities obtained via the direct Bethe ansatz such as the occupation of the resonant level as a function of the local chemical potential do match the numerical results. The case of one lead is studied in the most detail, with many results also extending to multiple leads, although there still remain open questions in this case.