# Quantum Dot at a Luttinger liquid edge

## TL;DR

This paper provides an exact solution for a system where a quantum dot is coupled to a Luttinger liquid edge, revealing the flow from weak to strong coupling and identifying critical exponents across regimes.

## Contribution

It offers an exact Hamiltonian solution for a Luttinger liquid coupled to a quantum dot, including eigenstates and temperature-dependent properties, highlighting non-perturbative Kondo physics.

## Key findings

- System flows from weak to strong coupling for all bulk interactions.
- Exact dot occupation as a function of energy computed at all temperatures.
- Identification of critical exponents at different coupling regimes.

## Abstract

We study a system consisting of a Luttinger liquid coupled to a quantum dot on the boundary. The Luttinger liquid is expressed in terms of fermions interacting via density-density coupling and the dot is modeled as an interacting resonant level on to which the bulk fermions can tunnel. We solve the Hamiltonian exactly and construct all eigenstates. We study both the zero and finite temperature properties of the system, in particular we compute the exact dot occupation as a function of the dot energy in all parameter regimes. The system is seen to flow from weak to to strong coupling for all values of the bulk interaction, with the flow characterized by a non-perturbative Kondo scale. We identify the critical exponents at the weak and strong coupling regimes.