Spin in a fluctuating field: The Bose(+Fermi) Kondo models

Physical Review Research

Physical Review B, 2014

The spin-boson model, describing a two-level system coupled to a bath of harmonic oscillators, is a generic model for quantum dissipation, with manifold applications. It has also been studied as a simple example for an impurity quantum phase transition. Here we present a detailed study of a U(1)-symmetric two-bath spin-boson model, where two different components of an SU(2) spin 1/2 are coupled to separate dissipative baths. Non-trivial physics arises from the competition of the two dissipation channels, resulting in a variety of phases and quantum phase transitions. We employ a combination of analytical and numerical techniques to determine the properties of both the stable phases and the quantum critical points. In particular, we find a critical intermediate-coupling phase which is bounded by a continuous quantum phase transition which violates the quantum-to-classical correspondence.

Reviews of Modern Physics, 2007

This review discusses instabilities of the Fermi-liquid state of conduction electrons in metals with particular emphasis on magnetic quantum critical points. Both the existing theoretical concepts and experimental data on selected materials are presented; with the aim of assessing the validity of presently available theory. After briefly recalling the fundamentals of Fermi-liquid theory, the local Fermi-liquid state in quantum impurity

Physical Review B, 2009

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 ω 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 < s < 1, further increase in the impurity-bath coupling results in a continuous, zero-temperature transition to a broken-symmetry phase in which the ground-state impurity occupancyn d acquires an expectation value n d 0 = 1. The response of the impurity occupancy to a locally applied electric potential features the hyperscaling of critical exponents and ω/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.

Physical Review Letters, 2005

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 η(ω) ∝ ω s , of interest in connection with heavy-fermion criticality. For 0 < s < 1, an interacting critical point, characterized by hyperscaling of exponents and ω/T -scaling, describes a quantum phase transition between Kondo-screened and localized phases. Connection is made to other results for the BFKM and the spin-boson model.

Physical Review B, 2007

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 Γ(ω) ∝ |ω| r with r ≥ 0, and a bosonic bath spectral function B(ω) ∝ ω s with s ≥ −1. For r < 1 and max(0, 2r − 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.

Lecture Notes in Physics, 2010

In this paper we give a general introduction to quantum critical phenomena, which we practically illustrate by a detailed study of the low energy properties of the spin boson model (SBM), describing the dynamics of a spin 1/2 impurity (or more generically a two-level system) coupled to a bath of independent harmonic oscillators. We show that the behavior of the model is very sensitive to the bath spectrum, in particular how the properties of the quantum critical point in the SBM are affected by the functional form of the bath Density of States (DoS). To this effect, we review the renormalization group (RG) treatment of the SBM for various bath DoS, based on an unconventional Majorana representation of the spin 1/2 degree of freedom. We also discuss the derivation of Shiba's relation for the sub-ohmic SBM, and explicitely derive an effective action vindicating the quantum to classical mapping.

Physical Review B, 2002

We study the competition between the Kondo effect and frustrating exchange interactions in a Kondo-lattice model within a large-N dynamical mean-field theory. We find a T = 0 phase transition between a heavy Fermi-liquid and a spin-liquid for a critical value of the exchange Jc = T 0 K , the single-impurity Kondo temperature. Close to the critical point, the Fermi liquid coherence scale T ⋆ is strongly reduced and the effective mass strongly enhanced. The regime T > T ⋆ is characterized by spin-liquid magnetic correlations and non-Fermi-liquid properties. It is suggested that magnetic frustration is a general mechanism which is essential to explain the large effective mass of some metallic compounds such as LiV2O4.

Proceedings of the National Academy of Sciences, 2005

Considerable evidence exists for the failure of the traditional theory of quantum critical points, pointing to the need to incorporate novel excitations. The destruction of Kondo entanglement and the concomitant critical Kondo effect may underlie these emergent excitations in heavy fermion metals (a prototype system for quantum criticality), but the effect remains poorly understood. Here, we show how ferromagnetic single-electron transistors can be used to study this effect. We theoretically demonstrate a gate-voltage-induced quantum phase transition. The critical Kondo effect is manifested in a fractional-power-law dependence of the conductance on temperature ( T ). The AC conductance and thermal noise spectrum have related power-law dependences on frequency (ω) and, in addition, show an ω/ T scaling. Our results imply that the ferromagnetic nanostructure constitutes a realistic model system to elucidate magnetic quantum criticality that is central to the heavy fermions and other b...

Physical Review B, 2020

We study the behavior of the entropy of the pseudogap Bose-Fermi Kondo model within a dynamical large-N limit, where N is related to the symmetry group of the model. This model is a general quantum impurity model that describes a localized level coupled to a fermionic bath having a density of states that vanishes in a powerlaw fashion near the Fermi energy and to a bosonic bath possessing a powerlaw spectral density below a cutoff energy. As a function of the couplings to the baths various quantum phase transitions can occur. We study how the impurity entropy changes across these zero-temperature transitions and compare our results with predictions based on the gtheorem. This is accomplished by an analysis of the leading and sub-leading scaling behavior. Our analysis shows that the g-theorem does not apply to the pseudogap Bose-Fermi Kondo model at the large-N level. This inapplicability originates from an anomalous contribution to the scaling function in the hydrodynamic regime where kBT > ω which is absent in the quantum coherent regime, i.e., for kBT < ω. We also compare our results with those obtained for the Sachdev-Ye-Kitaev or SYK model.

Journal of Low Temperature Physics, 2010

We discuss the general theoretical arguments advanced earlier for the T = 0 global phase diagram of antiferromagnetic Kondo lattice systems, distinguishing between the established and the conjectured. In addition to the wellknown phase of a paramagnetic metal with a "large" Fermi surface (P L), there is also an antiferromagnetic phase with a "small" Fermi surface (AF S). We provide the details of the derivation of a quantum non-linear sigma-model (QNLσ M) representation of the Kondo lattice Hamiltonian, which leads to an effective field theory containing both low-energy fermions in the vicinity of a Fermi surface and low-energy bosons near zero momentum. An asymptotically exact analysis of this effective field theory is made possible through the development of a renormalization group procedure for mixed fermion-boson systems. Considerations on how to connect the AF S and P L phases lead to a global phase diagram, which not only puts into perspective the theory of local quantum criticality for antiferromagnetic heavy fermion metals, but also provides the basis to understand the surprising recent experiments in chemically-doped as well as pressurized YbRh 2 Si 2. We point out that the AF S phase still occurs for the case of an equal number of spin-1/2 local moments and conduction electrons. This observation raises the prospect for a global phase diagram of heavy fermion systems in the Kondo-insulator regime. Finally, we discuss the connection between the Kondo breakdown physics discussed

Nature, 2001

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¯uctuations 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 CeCu 6-x Au x 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 ®nding 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.

Physical Review B, 2010

We discuss how multichannel Kondo physics can arise in the setting of a localized level coupled to several bosonic Tomonaga-Luttinger liquid leads. We propose one physical realization involving ultracold bosonic atoms coupled to an atomic quantum dot, and a second, based on superconducting nanowires coupled to a Cooper-pair box. The corresponding zero-temperature phase diagram is determined via an interplay between Kondo-type phenomena arising from the dot and the consequences of direct inter-lead hopping, which can suppress the Kondo effect. We demonstrate that the multichannel Kondo state is stable over a wide range of parameters. We establish the existence of two nontrivial phase transitions, involving a competition between Kondo screening at the dot and strong correlations either within or between the leads (which respectively promote local numberand phase-pinning). These transitions coalesce at a self-dual multicritical point.

Physical Review Letters, 2005

The problem of a spin-1=2 magnetic impurity near an antiferromagnetic transition of the host lattice is shown to transform to a multichannel problem. A variety of fixed points is discovered asymptotically near the antiferromagnetic critical point. Among these is a new variety of stable fixed point of a multichannel Kondo problem which does not require channel isotropy. At this point Kondo screening disappears but coupling to spin fluctuations remains. In addition to its intrinsic interest, the problem is an essential ingredient in the problem of quantum critical points in heavy fermions.