Quantum Dot at a Luttinger liquid edge

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.

9 pages + appendices Published version

References in corpus (10)

• Many-Body Physics with Ultracold Gases
• Luttinger Liquid in the Core of Screw Dislocation in Helium-4
• Quantum Phase Transition in a Resonant Level Coupled to Interacting Leads
• Helium-4 Luttinger liquids in nanopores
• Evidence of Luttinger liquid behavior in one-dimensional dipolar quantum gases
• Deformed strings in the Heisenberg model
• Single Impurity In Ultracold Fermi Superfluids
• Critical Flow and Dissipation in a Quasi-One-Dimensional Superfluid
• Quantum impurity in a Luttinger liquid: Exact solution of the Kane-Fisher model
• Non Self-conjugate Strings, Singular Strings and Rigged Configurations in the Heisenberg Model

Cited by in corpus (14)

• Rise and fall of Yu-Shiba-Rusinov bound-states in charge conserving $s$-wave one-dimensional superconductors
• Kondo effect in the isotropic Heisenberg spin chain
• Exact equilibrium results in the Interacting Resonant Level Model
• Transport and entanglement across integrable impurities from Generalized Hydrodynamics
• Quantum Dot in Interacting Environments
• Non-Abelian bosonization in a (3+1)-d Kondo semimetal via quantum anomalies
• Two-wire Junction of Inequivalent Tomonaga-Luttinger Liquids
• Many-body wavefunctions for quantum impurities out of equilibrium. II. Charge fluctuations
• Many-body wavefunctions for quantum impurities out of equilibrium
• Generalization of Lieb-Wu wave function inspired by one-dimensional ionic Hubbard model
• Realizing the interacting resonant level model using a quantum dot detector
• Local density of states of the interacting resonant level model at zero temperature
• From Luttinger liquids to Luttinger droplets via higher-order bosonization identities
• Generalized Calogero-Sutherland models for Kondo physics in the Luttinger liquid