Phase boundaries of the pseudogap Anderson and Kondo models

Abstract

We use the poor man's scaling approach to study the phase boundaries of a pair of quantum impurity models featuring a power-law density of states $\rho (\omega )\propto |\omega {|}^r$ that gives rise to quantum phase transitions between local-moment and Kondo-screened phases. For the Anderson model with a pseudogap (i.e., $r>0$), we find the phase boundary for (a) $0<r<1/2$, a range over which the model exhibits interacting quantum critical points both at and away from particle-hole symmetry, and (b) $r>1$, where the phases are separated by first-order quantum phase transitions. For the particle-hole-symmetric Kondo model with easy-axis or easy-plane anisotropy of the spin exchange, the phase boundary and scaling trajectories are obtained for both $r>0$ and $r<0$ (the later case describing a density of states that diverges at the Fermi energy). Comparison with nonperturbative results from the numerical renormalization group shows that poor man's scaling correctly describes the shape of phase boundaries expressed as functional relations between model parameters.

References in corpus (8)

• The electronic properties of graphene
• The numerical renormalization group method for quantum impurity systems
• Phase transitions in the pseudogap Anderson and Kondo models: Critical dimensions, renormalization group, and local-moment criticality
• Upper-critical dimension in a quantum impurity model: Critical theory of the asymmetric pseudogap Kondo problem
• Critical properties of the Fermi-Bose Kondo and pseudogap Kondo models: Renormalized perturbation theory
• Quantum phase transitions in a pseudogap Anderson-Holstein model
• Critical charge fluctuations in a pseudogap Anderson model
• Spin-anisotropic magnetic impurity in a Fermi gas: poor man's scaling equation integration

Cited by in corpus (6)

• Scaling theory of intrinsic Kondo and Hund's rule interactions in magic-angle twisted bilayer graphene
• Poor man's scaling: anisotropic Kondo and Coqblin--Schrieffer models
• Kondo screening regimes in multi-Dirac and Weyl systems
• Reentrant Kondo effect in a quantum impurity coupled to a metal-semiconductor hybrid contact
• Sublattice symmetry breaking and Kondo-effect enhancement in strained graphene
• Quantum criticality in the spin-isotropic pseudogap Bose-Fermi Kondo model: entropy, scaling, and the g-theorem