Matthew T. Glossop

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.

Magnetic quantum phase transition in an anisotropic kondo lattice.

The quantum phase transition between paramagnetic and antiferromagnetic phases of the Kondo lattice model with Ising anisotropy in the intersite exchange is studied within extended dynamical mean-field theory. Nonperturbative numerical solutions at zero temperature point to a continuous transition for both two- and three-dimensional magnetism. In the former case, the transition is associated with critical local physics, characterized by a vanishing Kondo scale and by an anomalous exponent in the dynamics close in value to that measured in heavy-fermion CeCu5.9Au0.1.

Kondo physics and dissipation: A numerical renormalization-group approach to Bose-Fermi Kondo models

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 s . The method is valid for all bath exponents s and all temperatures T. For 0s 1, the range of interest in the context of heavy-fermion quantum criticality, an interacting critical point, characterized by hyperscaling of exponents and /T scaling, describes a continuous quantum phase transition between Kondo-screened and localized phases. For Ohmic dissipation s =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.

Critical Kondo Destruction in a Pseudogap Anderson Model: Scaling and Relaxational Dynamics

We study the pseudogap Anderson model as a prototype system for critical Kondo destruction. We obtain finite-temperature (T) scaling functions near its quantum-critical point, by using a continuous-time quantum Monte Carlo method and also considering a dynamical large-N limit. We are able to determine the behavior of the scaling functions in the typically difficult to access quantum-relaxational regime (ℏω<k(B)T) and conclude that the relaxation rates for both the spin and single-particle excitations are linear in temperature. We discuss the implications of these results for the quantum-critical phenomena in heavy-fermion metals.

Quantum phase transitions in a charge-coupled Bose-Fermi Anderson model

We study the competition between Kondo physics and dissipation within an Anderson model of a magnetic impurity level that hybridizes with a metallic host and is also coupled, via the impurity charge, to the displacement of a bosonic bath having a spectral density proportional to \omega^s. As the impurity-bath coupling increases from zero, the effective Coulomb interaction between two electrons in the impurity level is progressively renormalized from its repulsive bare value until it eventually becomes attractive. For weak hybridization, this renormalization in turn produces a crossover from a conventional, spin-sector Kondo effect to a charge Kondo effect. At particle-hole symmetry, and for sub-Ohmic bath exponents 0 _0 \ne 1. The response of the impurity occupancy to a locally applied electric potential features the hyperscaling of critical exponents and \omega/T scaling that are expected at an interacting critical point. The numerical values of the critical exponents suggest that the transition lies in the same universality class as that of the sub-Ohmic spin-boson model. For the Ohmic case s = 1, the transition is instead of Kosterlitz-Thouless type. Away from particle-hole symmetry, the quantum phase transition is replaced by a smooth crossover, but signatures of the symmetric quantum critical point remain in the physical properties at elevated temperatures and/or frequencies.

Quantum phase transitions in a resonant-level model with dissipation: Renormalization-group studies

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 r , with r 0, and a bosonic-bath spectral function B s , with s �1. For r 1 and max 0,2 r �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 = 0, this model’s critical properties coincide with those of the spin-boson and Ising Bose-Fermi Kondo models, as expected from bosonization.

Continuous-Time Monte Carlo study of the pseudogap Bose-Fermi Kondo model

We study the pseudogap Bose-Fermi Anderson model with a continuous-time quantum Monte Carlo (CT-QMC) method. We discuss some delicate aspects of the transformation from this model to the Bose-Fermi Kondo model. We show that the CT-QMC method can be used at sufficiently low temperatures to access the quantum critical properties of these models.

Kondo physics in a dissipative environment

Abstract We report nonperturbative results for the interacting quantum-critical behavior in a Bose–Fermi Kondo model describing a spin- 1 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.