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

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##### Citation

Pixley, J. H., Kirchner, S., Ingersent, K., & Si, Q. (2013). Quantum criticality
in the pseudogap Bose-Fermi Anderson and Kondo models: Interplay between fermion- and boson-induced Kondo destruction.* Physical Review B,* *88*(24): 245111, pp. 1-15. doi:10.1103/PhysRevB.88.245111.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0017-C017-B

##### 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 | is an element of | r at the Fermi
energy (is an element of = 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.