Density of states of a dissipative quantum dot coupled to a quantum wire

TL;DR

This paper investigates the local density of states of a quantum dot coupled to a Luttinger liquid or quantum Hall edge, revealing power-law behaviors influenced by interactions and dissipation, with implications for understanding quantum impurity systems.

Contribution

It demonstrates that the density of states near the Fermi energy exhibits universal power-law behavior, largely independent of certain interactions, contrasting with thermodynamic properties like occupancy.

Findings

Density of states shows power-law frequency dependence near Fermi energy.

Behavior of the density of states can be insensitive to dot-lead interactions and dissipation.

Different models with same Fermi edge singularity exponents can have distinct density of states.

Abstract

We examine the local density of states of an impurity level or a quantum dot coupled to a fractional quantum Hall edge, or to the end of a single one-dimensional Luttinger-liquid lead. Effects of an Ohmic dissipative bath are also taken into account. Using both analytical and numerical techniques we show that, in general, the density of states exhibits power-law frequency dependence near the Fermi energy. In a substantial region of the parameter space it simply reflects the behavior of the tunneling density of states at the end of a Luttinger-liquid, and is insensitive either to the value of the dot-lead interaction or to the strength of dissipation; otherwise it depends on these couplings too. This behavior should be contrasted with the thermodynamic properties of the level, in particular, its occupancy, which were previously shown to depend on the various interactions in the system only through the corresponding Fermi edge singularity exponent, and thus cannot display any Luttinger-liquid specific power-law. Hence, we can construct different models, some with and some without interactions in the wire (but with equal Fermi edge singularity exponents), which would have very different level densities of states, although they all result in the same level population vs. energy curves.