Quantum criticality in the pseudogap Bose-Fermi Anderson and Kondo models: Interplay between fermion- and boson-induced Kondo destruction

TL;DR

This paper investigates the quantum critical behavior of impurity models with both fermionic and bosonic baths, revealing how each bath influences Kondo destruction and critical properties through advanced numerical methods.

Contribution

It provides a detailed analysis of the interplay between fermion- and boson-induced Kondo destruction using quantum Monte Carlo and renormalization-group techniques, identifying distinct critical regimes.

Findings

Identification of three critical regimes dominated by bosonic, fermionic, or mixed effects.

Observation of hyperscaling and mf5 scaling at the quantum critical point.

Good agreement between quantum Monte Carlo and renormalization-group results.

Abstract

We address the phenomenon of critical Kondo destruction in pseudogap Bose-Fermi Anderson and Kondo quantum impurity models. These models describe a localized level coupled both to a fermionic bath having a density of states that vanishes like |\epsilon|^r at the Fermi energy (\epsilon=0) and, via one component of the impurity spin, to a bosonic bath having a sub-Ohmic spectral density proportional to |\omega|^s. Each bath is capable by itself of suppressing the Kondo effect at a continuous quantum phase transition. We study the interplay between these two mechanisms for Kondo destruction using continuous-time quantum Monte Carlo for the pseudogap Bose-Fermi Anderson model with 0<r<1/2 and 1/2<s<1, and applying the numerical renormalization-group to the corresponding Kondo model. At particle-hole symmetry, the models exhibit a quantum critical point between a Kondo (fermionic strong-coupling) phase and a localized (Kondo-destroyed) phase. The two solution methods, which are in good agreement in their domain of overlap, provide access to the many-body spectrum, as well as to correlation functions including, in particular, the single-particle Green's function and the static and dynamical local spin susceptibilities. The quantum-critical regime exhibits the hyperscaling of critical exponents and \omega/T scaling in the dynamics that characterize an interacting critical point. The (r,s) plane can be divided into three regions: one each in which the calculated critical properties are dominated by the bosonic bath alone or by the fermionic bath alone, and between these two regions, a third in which the bosonic bath governs the critical spin response but both baths influence the renormalization-group flow near the quantum critical point.