Interacting resonant level coupled to a Luttinger liquid: Universality of thermodynamic properties

TL;DR

This paper shows that thermodynamic properties of a resonant level coupled to a Luttinger liquid are universal and unaffected by interaction details, using a Coulomb gas mapping and numerical validation.

Contribution

It introduces a Coulomb gas mapping for the model, revealing universality of thermodynamic properties regardless of interaction specifics.

Findings

Thermodynamic properties are universal across different interaction strengths.

The Coulomb gas approach captures the model's physics effectively.

Luttinger liquid effects do not alter these thermodynamic properties qualitatively.

Abstract

We investigate a model of a single resonant level coupled to the edge of a quantum wire in the Luttinger liquid phase or to the middle of a chiral Luttinger liquid via both tunneling and a contact interaction. Utilizing the Yuval-Anderson approach, we map this model onto a classical 1D Coulomb gas in which all the details of both the interactions in the lead and the level-lead interaction enter only through the corresponding Fermi-edge singularity exponent, which we explicitly evaluate using the Bethe ansatz solution for a particular model of the lead. Thus the population, dynamical capacitance and level entropy are universal in the sense of being equal for models with interactions differing in magnitude and even in sign. We demonstrate this to hold quantitatively using density matrix renormalization group calculations. Since the Coulomb gas description is of the single channel Kondo type, we infer that the universality we found implies that Luttinger liquid physics has no qualitative effect on these properties, in contrast with perturbative results.