Quantum Dot in Interacting Environments

Abstract

A quantum impurity attached to an interacting quantum wire gives rise to an array of of new phenomena. Using Bethe Ansatz we solve exactly models describing two geometries of a quantum dot coupled to an interacting quantum wire: a quantum dot that is (i) side-coupled and (ii) embedded in a Luttinger liquid. We find the eigenstates and determine the spectrum through the Bethe Ansatz equations. Using this we derive exact expressions for the ground state dot occupation. The thermodynamics are then studied using the thermodynamics Bethe Ansatz equations. It is shown that at low energies the dot becomes fully hybridized and acts as a backscattering impurity or tunnel junction depending on the geometry and furthermore that the two geometries are related by changing the sign of the interactions. Although remaining strongly coupled for all values of the interaction in the wire, there exists competition between the tunneling and backscattering leading to a suppression or enhancement of the dot occupation depending on the sign of the bulk interactions.

13 pages, v2 expanded and more calculations added

References in corpus (11)

• Many-Body Physics with Ultracold Gases
• 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
• Single Impurity In Ultracold Fermi Superfluids
• Quantum Wire Hybridized with a Single-Level Impurity
• Quantum impurity in a Luttinger liquid: Exact solution of the Kane-Fisher model
• Critical Flow and Dissipation in a Quasi-One-Dimensional Superfluid
• Quantum Dot at a Luttinger liquid edge
• Charging of a quantum dot coupled to Luttinger liquid leads
• Measuring Luttinger Liquid Correlations from Charge Fluctuations in a Nanoscale Structure

Cited by in corpus (7)

• 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 Boundary Modes in an Interacting Quantum Wire
• Transport and entanglement across integrable impurities from Generalized Hydrodynamics
• Non-Abelian bosonization in a (3+1)-d Kondo semimetal via quantum anomalies
• From Luttinger liquids to Luttinger droplets via higher-order bosonization identities
• Generalized Calogero-Sutherland models for Kondo physics in the Luttinger liquid