Interacting resonant level coupled to a Luttinger liquid: Universality of thermodynamic properties

Abstract

We investigate a model of a single resonant level coupled to the edge of a quantum wire in the Luttinger liquid phase or to the middle of a chiral Luttinger liquid via both tunneling and a contact interaction. Utilizing the Yuval-Anderson approach, we map this model onto a classical 1D Coulomb gas in which all the details of both the interactions in the lead and the level-lead interaction enter only through the corresponding Fermi-edge singularity exponent, which we explicitly evaluate using the Bethe ansatz solution for a particular model of the lead. Thus the population, dynamical capacitance and level entropy are universal in the sense of being equal for models with interactions differing in magnitude and even in sign. We demonstrate this to hold quantitatively using density matrix renormalization group calculations. Since the Coulomb gas description is of the single channel Kondo type, we infer that the universality we found implies that Luttinger liquid physics has no qualitative effect on these properties, in contrast with perturbative results.

6 pages, 2 figures; v3: published version

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Cited by in corpus (20)

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• Anderson Orthogonality in the Dynamics After a Local Quantum Quench
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• Quantum Dot at a Luttinger liquid edge
• Effect of a Coulombic dot-lead coupling on the dynamics of a quantum dot
• Interacting resonant level coupled to a Luttinger liquid: Population vs. density of states
• Exact equilibrium results in the Interacting Resonant Level Model
• Capacitance of a resonant level coupled to Luttinger liquids
• Entanglement entropy and quantum phase transitions in quantum dots coupled to Luttinger liquid wires
• Quantum Dot in Interacting Environments
• Exotic resonant level models in non-Abelian quantum Hall states coupled to quantum dots
• Transport through a quantum dot with two parallel Luttinger liquid leads
• Transport through a quantum dot with excitonic dot-lead coupling
• Density of states of a dissipative quantum dot coupled to a quantum wire
• Driven quantum dot coupled to a fractional quantum Hall edge
• Realizing the interacting resonant level model using a quantum dot detector
• Non-Fermi Liquid Quantum Impurity Physics from non-Abelian Quantum Hall States
• Local density of states of the interacting resonant level model at zero temperature
• Non-Fermi-liquid Kondo screening under Rabi driving