Rigorous Wilsonian Renormalization Group for impurity models with a spectral gap

Abstract

The Anderson impurity model (AIM) has long served as a cornerstone in the study of correlated electron systems. While numerical renormalization group (RG) offers great flexibility for metallic reservoirs, it becomes impossible in an unbiased way when a spectral gap $\Delta$ opens up in the tunneling density of states. The only known exception is provided by the superconducting bath. In this paper, we lift these limitations by a novel numerical RG procedure that employs a discretization of the gapped tunneling densities of states into patches which accumulate at the gap edges. This reveals an unusual double scaling which is a shared behavior by the superconducting and the scalar gapped AIMs. Moreover, it requires a special iterative diagonalization procedure with an alternating scheme for discarding states only every second iteration. The discretization and the diagonalization scheme form together, what we refer to as, the log-gap numerical RG. It is successfully applied to the superconducting and to the scalar gapped AIM. Consequently, it reveals that both models belong to the same RG equivalence class which manifests physically in common singlet-doublet quantum phase transitions accompanied by in-gap bound states of given parities. While superconducting AIM is mainly used for benchmarking of the log-gap numerical RG, we also rigorously confirm the phenomenon of in-gap states escaping into the continuum, which was recently indirectly considered in Ref. [1]. The gapped AIM is then tackled in a first ever exact numerical RG approach and confirms quantitatively assertions based on models with auxiliary metallic leads [2-5]. Moreover, it reveals that calculations performed in Refs. [6-8] are of strictly approximate nature.

arXiv comment16 pages, 10 figures

References in corpus (29)

• A Tunable Kondo Effect in Quantum Dots
• Continuous-time Monte Carlo methods for quantum impurity models
• The numerical renormalization group method for quantum impurity systems
• Kondo effect in quantum dots
• Self-consistent description of Andreev bound states in Josephson quantum dot devices
• Single magnetic adsorbates on s-wave superconductors
• Density matrix numerical renormalization group for non-Abelian symmetries
• Yu-Shiba-Rusinov screening of spins in double quantum dots
• The Anderson-Josephson quantum dot -- A theory perspective
• Numerical renormalization group calculation of near-gap peaks in spectral functions of the Anderson model with superconducting leads
• Kondo blockade due to quantum interference in single-molecule junctions
• Adaptive logarithmic discretization for numerical renormalization group methods
• The fate of the Kondo cloud in a superconductor
• Analytic impurity solver with the Kondo strong-coupling asymptotics
• Kondo Effect in Fermi Systems with a Gap: A Renormalization Group Study
• Quantum dot attached to superconducting leads: Relation between symmetric and asymmetric coupling
• Extremely correlated Fermi liquid theory meets Dynamical mean-field theory: Analytical insights into the doping-driven Mott transition
• Anderson impurity in a semiconductor
• Generalized atomic limit of a double quantum dot coupled to superconducting leads
• Spectral and transport properties of a half-filled Anderson impurity coupled to phase-biased superconducting and metallic leads
• Solution of the Anderson impurity model via the functional renormalization group
• Tunable reentrant Kondo effect in quantum dots coupled to metal-superconducting hybrid reservoirs
• Quantum phase transition in a gapped Anderson model: A numerical renormalization group study
• Quantum impurities in channel mixing baths
• Strongly correlated electrons: Analytic mean-field theories with two-particle self-consistency
• Reentrant Kondo effect in a quantum impurity coupled to a metal-semiconductor hybrid contact
• Unified theory of quantum phase transitions in quantum dots with gapped host bands
• Effective low-energy models for superconducting impurity systems
• Functional Integral Approach to the Single Impurity Anderson Model

Cited by in corpus (9)

• Suppressed Kondo screening in two-dimensional altermagnets
• Double-quantum-dot Andreev molecules: Phase diagrams and critical evaluation of effective models
• Hidden symmetry in interacting-quantum-dot-based multi-terminal Josephson junctions
• Andreev bound state spectroscopy of a quantum-dot-based Aharonov-Bohm interferometer with superconducting terminals
• Scalable Effective Models for Superconducting Nanostructures: Applications to Double, Triple, and Quadruple Quantum Dots
• Renormalized and iterative formalism of the Andreev levels within large multi-parametric space
• Quantum phase transition in a double quantum dot Josephson junction driven by electron-electron interactions
• Magnetic flux controlled current phase relationship in double Quantum Dot Josephson junction
• Effects of electron-electron interaction and spin-orbit coupling on Andreev pair qubits in quantum dot Josephson junctions