Validity of the local self-energy approximation: Application to coupled quantum impurities

Abstract

We examine the quality of the local self-energy approximation, applied here to models of multiple quantum impurities coupled to an electronic bath. The local self-energy is obtained by solving a single-impurity Anderson model in an effective medium that is determined self-consistently, similar to the dynamical mean-field theory (DMFT) for correlated lattice systems. By comparing to exact results obtained using the numerical renormalization group, we determine situations where "impurity-DMFT" is able to capture the physics of highly inhomogeneous systems, and those cases where it fails. For two magnetic impurities separated in real-space, the onset of the dilute limit is captured, but RKKY-dominated inter-impurity singlet formation cannot be described. For parallel quantum dot devices, impurity-DMFT succeeds in capturing underscreened Kondo physics by self-consistent generation of a critical pseudogapped effective medium. However, the quantum phase transition between high- and low-spin states on tuning interdot coupling cannot be described.

13 pages, 9 figures

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• Emergent Coherent Lattice Behavior in Kondo Nanosystems
• The Mott transition as a topological phase transition
• Strongly correlated multi-impurity models: The crossover from a single-impurity problem to lattice models
• Quantum impurities in channel mixing baths
• Open Wilson chains for quantum impurity models: Keeping track of all bath modes
• Magnetic Kondo regimes in a frustrated half-filled trimer
• Quantum spin liquid in an RKKY-coupled two-impurity Kondo system
• Kondo holes in strongly correlated impurity arrays: RKKY driven Kondo screening and hole-hole interactions
• Gutzwiller variational approach to the two-impurity Anderson model at particle-hole symmetry
• Non-interacting two-impurity Anderson model on a lattice at particle-hole symmetry
• Functional renormalization group study of parallel double quantum dots: Effects of asymmetric dot-lead couplings
• Interaction induced local moments in parallel quantum dots within the functional renormalization group approach
• On the competition between the Kondo effect and the exchange interaction in a parallel double quantum dot system