Quantum phase transitions and thermodynamics of the power-law Kondo model

Abstract

We revisit the physics of a Kondo impurity coupled to a fermionic host with a diverging power-law density of states near the Fermi level, $\rho (\omega )\sim |\omega {|}^r$, with exponent $-1<r<0$. Using the analytical understanding of several fixed points, based partially on powerful mappings between models with bath exponents $r$ and $(-r)$, combined with accurate numerical renormalization group calculations, we determine thermodynamic quantities within the stable phases, and also near the various quantum phase transitions. Antiferromagnetic Kondo coupling leads to strong screening with a negative zero-temperature impurity entropy, while ferromagnetic Kondo coupling can induce a stable fractional spin moment. We formulate the quantum field theories for all critical fixed points of the problem, which are fermionic in nature and allow for a perturbative renormalization-group treatment.

13 pages, 11 figures

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• Kondo impurities in the Kitaev spin liquid: Numerical renormalization group solution and gauge-flux-driven screening
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• Mott quantum criticality in the one-band Hubbard model: Dynamical mean-field theory, power-law spectra, and scaling
• Kondo effect in twisted bilayer graphene
• Kondo effect at low electron density and high particle-hole asymmetry in 1D, 2D, and 3D
• Kondo screening regimes in multi-Dirac and Weyl systems
• Spin-anisotropic magnetic impurity in a Fermi gas: poor man's scaling equation integration
• Critical quasiparticles in single-impurity and lattice Kondo models
• Single-impurity Kondo physics at extreme particle-hole asymmetry
• One- and two-channel Kondo model with logarithmic Van Hove singularity: a numerical renormalization group solution
• The Aubry-Andre Anderson model: Magnetic impurities coupled to a fractal spectrum
• Quantum criticality in the spin-isotropic pseudogap Bose-Fermi Kondo model: entropy, scaling, and the g-theorem
• Two-channel charge-Kondo physics in graphene quantum dots
• Fractional Local Moment and High Temperature Kondo Effect in Rashba-Fermi Gases
• Quantum impurity with 2/3 local moment in 1D quantum wires: an NRG study
• Tunable quantum criticality and pseudocriticality across the fixed-point annihilation in the anisotropic spin-boson model