Kevin Ingersent

Locally critical quantum phase transitions in strongly correlated metals

When a metal undergoes a continuous quantum phase transition, non-Fermi-liquid behaviour arises near the critical point. All the low-energy degrees of freedom induced by quantum criticality are usually assumed to be spatially extended, corresponding to long-wavelength fluctuations of the order parameter. But this picture has been contradicted by the results of recent experiments on a prototype system: heavy fermion metals at a zero-temperature magnetic transition. In particular, neutron scattering from CeCu6-x Aux has revealed anomalous dynamics at atomic length scales, leading to much debate as to the fate of the local moments in the quantum-critical regime. Here we report our theoretical finding of a locally critical quantum phase transition in a model of heavy fermions. The dynamics at the critical point are in agreement with experiment. We propose local criticality to be a phenomenon of general relevance to strongly correlated metals.

Renormalization-group study of Anderson and Kondo impurities in gapless Fermi systems

dilute magnetic impurities in unconventional ( d- and p-wave! superconductors, ‘‘flux phases’’ of the twodimensional electron gas, and certain zero-gap semiconductors. For the nondegenerate Anderson model, the main effects of the depression of the low-energy scattering rate are the suppression of mixed valence in favor of local-moment behavior and a marked reduction in the exchange coupling on entry to the local-moment regime, with a consequent narrowing of the range of parameters within which the impurity spin becomes Kondo screened. The precise relationship between the Anderson model and the exactly screened Kondo model with power-law exchange is examined. The intermediate-coupling fixed point identified in the latter model by Withoff and Fradkin ~WF! is shown to have clear signatures both in the thermodynamic properties and in the local magnetic response of the impurity. The underscreened, impurity-spin-1 Kondo model and the overscreened, two-channel Kondo model both exhibit a conditionally stable intermediate-coupling fixed point in addition to unstable fixed points of the WF type. In all four models, the presence or absence of particle-hole symmetry plays a crucial role in determining the physics both at strong coupling and in the vicinity of the WF transition. These results are obtained using an extension of Wilson’s numerical renormalization-group technique to treat energy-dependent scattering. The strong- and weak-coupling fixed points of each model are identified and their stability is analyzed. Algebraic expressions are derived for the fixed-point thermodynamic properties and for low-temperature corrections about the stable fixed points. Numerical data are presented confirming the algebraic results, identifying and characterizing intermediate-coupling ~non-Fermi-liquid! fixed points, and exploring temperature-driven crossovers between different physical regimes. @S0163-1829~98!04222-2#

Zero-Field Kondo Splitting and Quantum-Critical Transition in Double Quantum Dots

Double quantum dots offer unique possibilities for the study of many-body correlations. A system containing one Kondo dot and one effectively noninteracting dot maps onto a single-impurity Anderson model with a structured (nonconstant) density of states. Numerical renormalization-group calculations show that, while band filtering through the resonant dot splits the Kondo resonance, the singlet ground state is robust. The system can also be continuously tuned to create a pseudogapped density of states and access a quantum-critical point separating Kondo and non-Kondo phases.

Critical local-moment fluctuations, anomalous exponents, and omega/T scaling in the Kondo problem with a pseudogap.

Experiments in heavy-fermion metals and related theoretical work suggest that critical local-moment fluctuations can play an important role near a zero-temperature phase transition. We study such fluctuations at the quantum critical point of a Kondo impurity model in which the density of band states vanishes as /epsilon/(r) at the Fermi energy (epsilon=0). The local spin response is described by a set of critical exponents that vary continuously with r. For 0<r<1, the dynamical susceptibility at the critical point exhibits omega/T scaling with a fractional exponent, implying that the critical point is interacting.

Kondo Screening in a Magnetically Frustrated Nanostructure: Exact Results on a Stable Non-Fermi-Liquid Phase

Triangular symmetry stabilizes a novel non-Fermi-liquid phase in the three-impurity Kondo model with frustrating antiferromagnetic interactions between half-integer impurity spins. The phase arises without fine-tuning of couplings, and is stable against magnetic fields and particle-hole symmetry breaking. We find a conformal field theory describing this phase, verify it using the numerical renormalization group, and extract various exact, universal low-energy properties. Signatures predicted in electrical transport may be testable in scanning tunneling microscopy or quantum-dot experiments.

Numerical Renormalization-Group Study of the Bose-Fermi Kondo 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 CRITICAL BEHAVIOR IN KONDO SYSTEMS

This article briefly reviews three topics related to the quantum critical behavior of certain heavy-fermion systems. First, we summarize an extended dynamical mean-field theory for the Kondo lattice, which treats on an equal footing the quantum fluctuations associated with the Kondo and RKKY couplings. The resulting dynamical mean-field equations describe a Kondo impurity model with an additional coupling to vector bosons. Two types of quantum phase transition appear to be possible within this approach — the first a conventional spin-density-wave transition, the second driven by local physics. For the second type of transition to be realized, the effective impurity model must have a quantum critical point exhibiting an anomalous local spin susceptibility. In the second part of the paper, such a critical point is shown to occur in two variants of the Kondo impurity problem. Finally, we propose an operational test for the existence of quantum critical behavior driven by local physics. Neutron scattering results suggest that CeCu6-xAux passes this test.

Behavior of magnetic impurities in gapless Fermi systems

In a number of systems, including certain semiconductors and unconventional superconductors, the effective density of states varies like |E-

Kondo destruction and valence fluctuations in an Anderson model.

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