Interacting resonant level coupled to a Luttinger liquid: Population vs. density of states

TL;DR

This paper investigates how a quantum dot coupled to a Luttinger liquid exhibits different behaviors in population and density of states, revealing that thermodynamic and dynamical properties depend differently on interactions.

Contribution

It demonstrates that population and density of states depend on interactions in distinct ways, with the population determined by a single exponent and the density of states showing diverse behaviors.

Findings

Population depends only on the Fermi edge singularity exponent.

Density of states can be regular or show power-law suppression/enhancement.

Results confirmed by DMRG and Monte Carlo simulations.

Abstract

We consider the problem of a single level quantum dot coupled to the edge of a one-dimensional Luttinger liquid wire by both a hopping term and electron-electron interactions. Using bosonization and Coulomb gas mapping of the Anderson-Yuval type we show that thermodynamic properties of the level, in particular, its occupation, depend on the various interactions in the system only through a single quantity --- the corresponding Fermi edge singularity exponent. However, dynamical properties, such as the level density of states, depend in a different way on each type of interaction. Hence, we can construct different models, with and without interactions in the wire, with equal Fermi edge singularity exponents, which have identical population curves, although they originate from very different level densities of states. The latter may either be regular or show a power-law suppression or enhancement at the Fermi energy. These predictions are verified to a high degree of accuracy using the density matrix renormalization group algorithm to calculate the dot occupation, and classical Monte Carlo simulations on the corresponding Coulomb gas model to extract the level density of states.