Interacting resonant level coupled to a Luttinger liquid: Population vs. density of states

Abstract

We consider the problem of a single level quantum dot coupled to the edge of a one-dimensional Luttinger liquid wire by both a hopping term and electron-electron interactions. Using bosonization and Coulomb gas mapping of the Anderson-Yuval type we show that thermodynamic properties of the level, in particular, its occupation, depend on the various interactions in the system only through a single quantity --- the corresponding Fermi edge singularity exponent. However, dynamical properties, such as the level density of states, depend in a different way on each type of interaction. Hence, we can construct different models, with and without interactions in the wire, with equal Fermi edge singularity exponents, which have identical population curves, although they originate from very different level densities of states. The latter may either be regular or show a power-law suppression or enhancement at the Fermi energy. These predictions are verified to a high degree of accuracy using the density matrix renormalization group algorithm to calculate the dot occupation, and classical Monte Carlo simulations on the corresponding Coulomb gas model to extract the level density of states.

6 pages, 2 figures; Proceedings of FQMT '08

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Cited by in corpus (13)

• Anderson Orthogonality in the Dynamics After a Local Quantum Quench
• Duality between different geometries of a resonant level in a Luttinger liquid
• Out-of-equilibrium properties and non-linear effects for interacting quantum impurity systems in their strong coupling regime
• Effect of a Coulombic dot-lead coupling on the dynamics of a quantum dot
• 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
• Transport through a quantum dot with two parallel Luttinger liquid leads
• Hierarchical equations of motion approach to transport through an Anderson impurity coupled to interacting Luttinger liquid leads
• Density of states of a dissipative quantum dot coupled to a quantum wire
• Transport through a quantum dot with excitonic dot-lead coupling
• Driven quantum dot coupled to a fractional quantum Hall edge
• Local density of states of the interacting resonant level model at zero temperature