Quantum criticality in the spin-isotropic pseudogap Bose-Fermi Kondo model: entropy, scaling, and the g-theorem

Abstract

We study the behavior of the entropy of the pseudogap Bose-Fermi Kondo model within a dynamical large-$N$ limit, where $N$ is related to the symmetry group of the model. This model is a general quantum impurity model that describes a localized level coupled to a fermionic bath having a density of states that vanishes in a powerlaw fashion near the Fermi energy and to a bosonic bath possessing a powerlaw spectral density below a cutoff energy. As a function of the couplings to the baths various quantum phase transitions can occur. We study how the impurity entropy changes across these zero-temperature transitions and compare our results with predictions based on the g-theorem. This is accomplished by an analysis of the leading and sub-leading scaling behavior. Our analysis shows that the $g$-theorem does not apply to the pseudogap Bose-Fermi Kondo model at the large-N level. This inapplicability originates from an anomalous contribution to the scaling function in the hydrodynamic regime where $k_{B}T>\hslash \omega$ which is absent in the quantum coherent regime, i.e., for $k_{B}T<\hslash \omega$. We also compare our results with those obtained for the Sachdev-Ye-Kitaev model.

References in corpus (19)

• Weak magnetism and non-Fermi liquids near heavy-fermion critical points
• Numerical Renormalization Group for Bosonic Systems and Application to the Subohmic Spin-Boson Model
• Frustration and the Kondo effect in heavy fermion materials
• Fermi-surface collapse and dynamical scaling near a quantum critical point
• The g-theorem and quantum information theory
• Quantum phase transitions in the Bose-Fermi Kondo model
• Zero-field Kondo splitting and quantum-critical transition in double quantum dots
• Quantum critical properties of the Bose-Fermi Kondo Model in a large-N limit
• Sum Rules and Ward Identities in the Kondo Lattice
• Schwinger Boson approach to the fully screened Kondo model
• Universal crossovers and critical dynamics of quantum phase transitions: A renormalization group study of the pseudogap Kondo problem
• Quantum Criticality in Ferromagnetic Single-Electron Transistors
• Critical properties of the Fermi-Bose Kondo and pseudogap Kondo models: Renormalized perturbation theory
• Nonperturbative Scaling Theory of Free Magnetic Moment Phases in Disordered Metals
• Convergence acceleration and stabilization for dynamical-mean-field-theory calculations
• Scaling and Enhanced Symmetry at the Quantum Critical Point of the Sub-Ohmic Bose-Fermi Kondo Model
• The pseudogap Fermi-Bose Kondo model
• Kondo physics in a dissipative environment
• The Bose-Fermi Kondo model with a singular dissipative spectrum: Exact solutions and their implications

Cited by in corpus (1)

• Exact solutions of Kondo problems in higher-order fermions