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Bulletin of the American Physical Society

Kondo physics in a dissipative environment

Kevin Ingersent, Matthew T. Glossop, N. Khoshkhou

Published Mar 5, 2007• 0 citations
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Abstract

We report nonperturbative results for the interacting quantum-critical behavior in a Bose-Fermi Kondo model describing a spin1 2 coupled both to a fermionic band with a pseudogap density of states and to a dissipative bosonic bath. The model serves as a paradigm for studying the interplay between Kondo physics and low-energy dissipative modes in strongly correlated systems.

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We report nonperturbative results for the interacting quantum-critical behavior in a Bose-Fermi Kondo model describing a spin1 2 coupled both to a fermionic band with a pseudogap density of states and to a dissipative bosonic bath. The model serves as a paradigm for studying the interplay between Kondo physics and low-energy dissipative modes in strongly correlated systems.
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 ${|\ensuremath{\epsilon}|}^{r}$ at the Fermi energy ($\ensuremath{\epsilon}=0$) and, via one component of the impurity spin, to a bosonic bath having a sub-Ohmic spectral density proportional to ${|\ensuremath{\omega}|}^{s}$. 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<120<r<\frac{1}{2}0<r<21​ and $\frac{1}{2}\ensuremath{\le}s<1$, 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 $\ensuremath{\omega}/T$ scaling in the dynamics that characterize an interacting critical point. The (r,s)(r,s)(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.
We extend the numerical renormalization-group method to treat Bose-Fermi Kondo models (BFKMs) describing a local moment coupled both to a conduction band and to a dissipative bosonic bath representing, e.g., lattice or spin collective excitations of the environment. We apply the method to the Ising-symmetry BFKM with a structureless band and a bath spectral function $\ensuremath{\eta}(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\omega}}^{s}$. The method is valid for all bath exponents sss and all temperatures TTT. For 0<s<10<s<10<s<1, the range of interest in the context of heavy-fermion quantum criticality, an interacting critical point, characterized by hyperscaling of exponents and $\ensuremath{\omega}∕T$ scaling, describes a continuous quantum phase transition between Kondo-screened and localized phases. For Ohmic dissipation s=1s=1s=1, where the model is relevant to certain dissipative mesoscopic qubit devices, the transition is found to be Kosterlitz-Thouless-like. In both regimes the impurity spectral function for the corresponding Anderson model shows clearly the collapse of the Kondo resonance at the transition. Connection is made to other recent results for the BFKM and the spin-boson model.
We extend the numerical renormalization-group method to Bose-Fermi Kondo models (BFKMs), describing a local moment coupled to a conduction band and a dissipative bosonic bath. We apply the method to the Ising-symmetry BFKM with a bosonic bath spectral function eta(omega) proportional omega(s), of interest in connection with heavy-fermion criticality. For 0 < s < 1, an interacting critical point, characterized by hyperscaling of exponents and omega/T scaling, describes a quantum phase transition between Kondo-screened and localized phases. A connection is made to other results for the BFKM and the spin-boson model.
Quantum dissipation induces a critical destruction of a Kondo screened state, which is of interest in the contexts of quantum critical heavy fermion metals and magnetic nanostructures. The sub-ohmic Bose-Fermi Kondo model provides a setting to study this effect. We find that this many-body problem is exactly solvable when the spectrum of the dissipative bosonic bath, J(ω), is singular, corresponding to J(τ)=const.. We determine the local spin correlation functions, showing that the singular LONGITUDINAL fluctuations of the bosonic bath dominate over the transverse ones. Our results provide evidence that the local quantum critical solution, derived within the extended dynamical mean field approach to the Kondo lattice model, has a zero residual entropy.
We study a spinless level that hybridizes with a fermionic band and is also coupled via its charge to a dissipative bosonic bath. We consider the general case of a power-law hybridization function $\ensuremath{\Gamma}(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\mid}\ensuremath{\omega}\ensuremath{\mid}}^{r}$, with $r\ensuremath{\geqslant}0$, and a bosonic-bath spectral function $B(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\omega}}^{s}$, with $s\ensuremath{\geqslant}\ensuremath{-}1$. For r<1r<1r<1 and $\mathrm{max}(0,2r\ensuremath{-}1)<s<1$, this Bose-Fermi quantum impurity model features a continuous zero-temperature transition between a delocalized phase, with tunneling between the impurity level and the band, and a localized phase, in which dissipation suppresses tunneling in the low-energy limit. The phase diagram and the critical behavior of the model are elucidated using perturbative and numerical renormalization-group techniques, between which there is excellent agreement in the appropriate regimes. For r=0r=0r=0, this model's critical properties coincide with those of the spin-boson and Ising Bose-Fermi Kondo models, as expected from bosonization.
Quantum criticality that goes beyond the Landau framework of order-parameter fluctuations is playing a central role in elucidating the behavior of strange metals. A prominent case appears in Kondo lattice systems, which have been extensively analysed in terms of an effective Bose-Fermi Kondo model. Here, a spin is simultaneously coupled to conduction electron bands and gapless vector bosons that represent magnetic fluctuations. The Bose-Fermi Kondo model features interacting fixed points of Kondo destruction with such properties as dynamical Planckian (ℏω/kBT\hbar ω/ k_{\rm B} Tℏω/kB​T) scaling and loss of quasiparticles. Here we carry out a renormalization-group analysis of the model with spin isotropy and identify pair-wise annihilations of the fixed points as the spectrum of the bosonic bath evolves. Our analysis not only provides an essentially complete understanding of the previous numerical results of an SU(2)-symmetric model, but also reveals a surprising feature of sequential fixed-point annihilation. Our results lay the foundation for the understanding of quantum criticality in spin-isotropic heavy-fermion metals as well as in doped Mott-Hubbard systems.