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arXiv:1904.11471

Dynamical Kondo effect and Kondo destruction in effective models for quantum-critical heavy fermion metals

Ang Cai, Haoyu Hu, Kevin Ingersent, Silke Buehler Paschen, Qimiao Si A

Published Apr 25, 2019• 7 citations
arXivHTMLPDF

Abstract

Quantum criticality in certain heavy-fermion metals is believed to go beyond the Landau framework of order-parameter fluctuations. In particular, there is considerable evidence for Kondo destruction: a disappearance of the static Kondo singlet amplitude that results in a sudden reconstruction of Fermi surface across the quantum critical point and an extra critical energy scale. This effect can be analyzed in terms of a dynamical interplay between the Kondo and RKKY interactions. In the Kondo-destroyed phase, a well-defined Kondo resonance is lost, but Kondo singlet correlations remain at nonzero frequencies. This dynamical effect allows for mass enhancement in the Kondo-destroyed phase. Here, we elucidate the dynamical Kondo effect in Bose-Fermi Kondo/Anderson models, which unambiguously exhibit Kondo-destruction quantum critical points. We show that a simple physical quantity---the expectation value $\langle {\bf S}_{f} \cdot {\bf s}_{c} \rangle$ for the dot product of the local ($f$) and conduction-electron ($c$) spins---varies continuously across such quantum critical points. A nonzero $\langle {\bf S}_{f} \cdot {\bf s}_{c} \rangle$ manifests the dynamical Kondo effect that operates in the Kondo-destroyed phase. Implications are discussed for the stability of Kondo-destruction quantum criticality as well as the understanding of experimental results in quantum critical heavy-fermion metals.

DOI
10.48550/arxiv.1904.11471

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Quantum criticality in certain heavy-fermion metals is believed to go beyond the Landau framework of order-parameter fluctuations. In particular, there is considerable evidence for Kondo destruction: a disappearance of the static Kondo singlet amplitude that results in a sudden reconstruction of Fermi surface across the quantum critical point and an extra critical energy scale. This effect can be analyzed in terms of a dynamical interplay between the Kondo and RKKY interactions. In the Kondo-destroyed phase, a well-defined Kondo resonance is lost, but Kondo singlet correlations remain at nonzero frequencies. This dynamical effect allows for mass enhancement in the Kondo-destroyed phase. Here, we elucidate the dynamical Kondo effect in Bose-Fermi Kondo/Anderson models, which unambiguously exhibit Kondo-destruction quantum critical points. We show that a simple physical quantity---the expectation value ⟨Sf⋅sc⟩\langle {\bf S}_{f} \cdot {\bf s}_{c} \rangle⟨Sf​⋅sc​⟩ for the dot product of the local (fff) and conduction-electron (ccc) spins---varies continuously across such quantum critical points. A nonzero ⟨Sf⋅sc⟩\langle {\bf S}_{f} \cdot {\bf s}_{c} \rangle⟨Sf​⋅sc​⟩ manifests the dynamical Kondo effect that operates in the Kondo-destroyed phase. Implications are discussed for the stability of Kondo-destruction quantum criticality as well as the understanding of experimental results in quantum critical heavy-fermion metals.
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.
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.
Quantum critical points often arise in metals perched at the border of an antiferromagnetic order. The recent observation of singular and dynamically scaling charge conductivity in an antiferromagnetic quantum critical heavy fermion metal implicates beyond-Landau quantum criticality. Here we study the charge and spin dynamics of a Kondo destruction quantum critical point (QCP), as realized in an SU(2)-symmetric Bose-Fermi Kondo model. We find that the critical exponents and scaling functions of the spin and single-particle responses of the QCP in the SU(2) case are essentially the same as those of the large-N limit, showing that 1/N corrections are subleading. Building on this insight, we demonstrate that the charge responses at the Kondo destruction QCP are singular and obey ω/T scaling. This property persists at the Kondo destruction QCP of the SU(2)-symmetric Kondo lattice model.
Strange metal behavior has been observed in an expanding list of quantum materials, with heavy fermion metals serving as a prototype setting. Among the intriguing questions is the nature of charge carriers; there is an increasing recognition that the quasiparticles are lost, as captured by Kondo destruction quantum criticality. Among the recent experimental advances is the measurement of shot noise in a heavy-fermion strange metal. We are thus motivated to study current fluctuations by advancing a minimal Bose-Fermi Kondo lattice model, which admits a well-defined large-NNN limit. Showing that the model in equilibrium captures the essential physics of Kondo destruction, we proceed to derive quantum kinetic equations and compute shot noise to the leading nontrivial order in 1/N1/N1/N. Our results reveal a strong suppression of the shot noise at the Kondo destruction quantum critical point, thereby providing the understanding of the striking experiment. Broader implications of our results are discussed.
In this thesis I investigate several aspects of local quantum criticality, a concept of key importance in a number of physical contexts ranging from critical heavy fermion compounds to quantum dot systems. Quantum critical points are associated with second order phase transitions at zero temperature. In contrast to their finite-temperature counterparts, the zero-point motion cannot be neglected near a quantum critical point. As a result, the incorporation of quantum dynamics leads to an effective dimension larger than the spatial dimension of the system for the order parameter fluctuations within the Ginzburg-Landau-Wilson treatment of criticality. This so-called quantum-to-classical mapping works well for the critical properties in insulating systems but apparently fails in systems containing gapless fermions. This has been experimentally most clearly been demonstrated within a particular class of intermetallic compounds called heavy fermions. A particular way in which the Ginzburg-Landau-Wilson paradigm fails is for critical Kondo destruction that seems to underlie the unconventional quantum criticality seen in the heavy fermions. I focus on studying the properties of critical Kondo destruction and the emergence of energy-over-temperature-scaling in systems without spatial degrees of freedom, i.e., so-called quantum impurity systems. In particular, I employ large-N techniques to address critical properties of this class of quantum phase transitions in and out of equilibrium. As quantum critical systems are characterized by a scale-invariant spectrum with many low-lying excitations, it may appear that any perturbation can lead to a response beyond the linear response regime. Understanding what governs the non-linear response regime near quantum criticality is an interesting area. Here, I first present a path integral version of the Schrieffer-Wolff transformation which relates the functional integral form of the partition function of the Anderson model to that of its effective low-energy model. The equivalence between the low-energy sector of the Anderson model in the Kondo regime and the spin-isotropic Kondo model is usually established via a canonical transformation performed on the Hamiltonian, followed by a projection. The resulting functional integral assumes the form of a spin path integral and includes a geometric phase factor, i.e. a Berry phase. The approach stresses the underlying symmetries of the model and allows for a straightforward generalization of the transformation to more involved models. As an example of the efficiency of the approach I apply it to a single electron transistor attached to ferromagnetic leads and derive the effective low-energy model of such a magnetic transistor. As Kondo screening is a local phenomenon, it and its criticality can be studied using the appropriate impurity model. A general impurity model to study critical Kondo destruction is the pseudogap Bose-Fermi Kondo model. Here, I concentrate on the multi-channel version of the model using the dynamical large-N study. This model allows to study the non-trivial interplay between two different mechanisms of critical Kondo destruction. The interplay of two processes that can each by itself lead to critical Kondo destruction. The zero-temperature residual entropy at various fixed points for the model is also discussed. The two channel Anderson model exhibits several continuous quantum phase transitions between weak- and strong-coupling phases. The non-crossing approximation (NCA) is believed to give reliable results for the standard two-channel Anderson model of a magnetic impurity in a metal. I revisit the reliability of the NCA for the standard two channel Anderson model (constant conduction electron density of states) and investigate its reliability for the two-channel pseudogap Anderson model. This is done by comparing finite-temperature, finite-frequency solutions of the NCA equations and asymptotically exact zero-temperature NCA solutions with numerical renormalization-group calculations. The phase diagram of this model is well established. The focus here will be on the dynamical scaling properties obtained within the NCA. Finally, I study the thermal and non-thermal steady state scaling functions and the steady-state dynamics of the pseudogap Kondo model. This model allows us to study the concept of effective temperatures near fully interacting as well as weak-coupling fixed points and compare the out-of-equilibrium scaling properties of critical Kondo destruction to those of the traditional spin-density wave (SDW) scenario. The differences I identify can be experimentally probed. This may be helpful in identifying the nature of the quantum critical points observed in certain heavy fermion compounds.
Recent studies of the global phase diagram of quantum-critical heavy-fermion metals prompt consideration of the interplay between the Kondo interactions and quantum fluctuations of the local moments alone. Toward this goal, we study a Bose-Fermi Kondo model (BFKM) with Ising anisotropy in the presence of a local transverse field that generates quantum fluctuations in the local-moment sector. We apply the numerical renormalization-group method to the case of a sub-Ohmic bosonic bath exponent and a constant conduction-electron density of states. Starting in the Kondo phase at zero transverse field, there is a smooth crossover with increasing transverse field from a fully screened to a fully polarized impurity spin. By contrast, if the system starts in its localized phase, then increasing the transverse field causes a continuous, Kondo-destruction transition into the partially polarized Kondo phase. The critical exponents at this quantum phase transition exhibit hyperscaling and take essentially the same values as those of the BFKM in zero transverse field. The many-body spectrum at criticality varies continuously with the bare transverse field, indicating a line of critical points. We discuss implications of these results for the global phase diagram of the Kondo lattice model.