The Fermi-liquid properties of a two-orbital impurity Anderson model with an f2 local singlet ground state is studied by the numerical renormalization group method. It is shown that a heavy-fermion (HF) state with a vanishingly small Wilson ratio is realized in the vicinity of the quantum critical point (QCP) between the local-singlet and Kondo-singlet phases. The parameter area in which the HF behavior appears is remarkably enlarged with increasing the excitation energy from the local singlet to triplet states. It is also clarified that the HF state takes place with an intermediate average occupancy of f electrons, reflecting the existence of the QCP under strong valence fluctuation. The possible application of these theoretical results to an unconventional HF state in Sm compounds is discussed.
The Fermi-liquid properties of a two-orbital impurity Anderson model with an f2 local singlet ground state is studied by the numerical renormalization group method. It is shown that a heavy-fermion (HF) state with a vanishingly small Wilson ratio is realized in the vicinity of the quantum critical point (QCP) between the local-singlet and Kondo-singlet phases. The parameter area in which the HF behavior appears is remarkably enlarged with increasing the excitation energy from the local singlet to triplet states. It is also clarified that the HF state takes place with an intermediate average occupancy of f electrons, reflecting the existence of the QCP under strong valence fluctuation. The possible application of these theoretical results to an unconventional HF state in Sm compounds is discussed.
An interplay of valence fluctuation and orbital occupancy is studied for a two-orbital impurity Anderson model having f2 singlet ground and triplet excited states in the localized limit. Employing the numerical renormalization group method, we identify the existence of a quantum phase transition between the local-singlet and the Kondo-singlet states in a variation of the c–f hybridization, and clarify how it depends on the f2 singlet–triplet energy splitting. It is found that the transition takes place definitely at a finite strength of the hybridization even when the singlet–triplet splitting is infinitely large. It is also found that as the splitting becomes small, the occupancies of the singlet and triplet states display a drastic change in the vicinity of the transition point. The origin of these findings is discussed in view of the features of valence fluctuation from the local many-body singlet state.
We investigate the emergence of quantum critical points near a two-channel Kondo phase by evaluating an f-electron entropy of a seven-orbital impurity Anderson model hybridized with three (Γ7 and Γ8) conduction bands with the use of a numerical renormalization group method First we consider the case of Pr3+ ion, in which quadrupole two-channel Kondo effect is known to occur for the local Γ3 doublet state. When we control crystalline electric field (CEF) potentials so as to change the local CEF ground state from Γ3 doublet to Γ1 singlet or Γ5 triplet, we commonly observe a residual entropy of logϕ with the golden ratio ϕ=(1+5)/2, which is equal to that for three-channel Kondo effect. This peculiar residual entropy is also observed for the case of Nd3+ ion, in which magnetic two-channel Kondo phase is found to occur for the local Γ6 doublet state. We envisage a scenario that the quantum critical point characterized by logϕ generally appears between two-channel Kondo and Fermi-liquid phases.
We study paramagnetic quantum criticality in the periodic Anderson model (PAM) using cellular dynamical mean-field theory (CDMFT), with the numerical renormalization group (NRG) as a cluster impurity solver. The PAM describes itinerant c electrons hybridizing with a lattice of localized f electrons. At zero temperature, it exhibits a much-studied quantum phase transition from a Kondo phase to a Ruderman-Kittel-Kasuya-Yosida (RKKY) phase when the hybridization is decreased through a so-called Kondo breakdown quantum critical point (KB QCP). There, Kondo screening of f spins by c electrons breaks down, so that f excitations change their character from somewhat itinerant to mainly localized, while c excitations remain itinerant. Building on , which interpreted the KB transition as an orbital-selective Mott transition, we here elucidate its nature in great detail by performing a high-resolution, real-frequency study of various dynamical quantities (susceptibilities, self-energies, and spectral functions). NRG allows us to study the quantum critical regime governed by the QCP and located between two temperature scales, T FL < T NFL . In this regime, we find fingerprints of non-Fermi-liquid (NFL) behavior in several dynamical susceptibilities. Surprisingly, CDMFT self-consistency is essential to stabilize the QCP and the NFL regime. The Fermi-liquid (FL) scale T FL decreases toward and vanishes at the KB QCP; at temperatures below T FL , FL behavior emerges. At T = 0 , we find the following properties. The KB transition is continuous. The f quasiparticle weight decreases continuously as the transition is approached from either side, vanishing only at the KB QCP. Therefore, the quasiparticle weight of the f band is nonzero not only in the Kondo phase, but also in the RKKY phase; hence, the FL quasiparticles comprise c f electrons in both phases. The Fermi surface (FS) volumes in the two phases differ, implying a FS reconstruction at the KB QCP. Whereas the large-FS Kondo phase has a two-band structure as expected, the small-FS RKKY phase unexpectedly has a three-band structure. We provide a detailed analysis of quasiparticle properties of both the Kondo and, for the first time, also the RKKY phase and uncover their differences. The FS reconstruction is accompanied by the appearance of a Luttinger surface on which the f self-energy diverges. The volumes of the Luttinger and Fermi surfaces are related to the charge density by a generalized Luttinger sum rule. We interpret the small FS volume and the emergent Luttinger surface as evidence for f -electron fractionalization in the RKKY phase. Finally, we compute the temperature dependence of the Hall coefficient and the specific heat, finding good qualitative agreement with experiments. Published by the American Physical Society 2024
We generalize Nozi\`eres' Fermi-liquid theory for the low-energy behavior of the Kondo model to that of the single-impurity Anderson model. In addition to the electrons' phase shift at the Fermi energy, the low-energy Fermi-liquid theory is characterized by four Fermi-liquid parameters: the two given by Nozi\`eres that enter to first order in the excitation energy, and two additional ones that enter to second order and are needed away from particle-hole symmetry. We express all four parameters in terms of zero-temperature physical observables, namely the local charge and spin susceptibilities and their derivatives with respect to the local level position. We determine these in terms of the bare parameters of the Anderson model using Bethe ansatz and numerical renormalization group (NRG) calculations. Our low-energy Fermi-liquid theory applies throughout the crossover from the strong-coupling Kondo regime via the mixed-valence regime to the empty-orbital regime. From the Fermi-liquid theory, we determine the conductance through a quantum dot symmetrically coupled to two leads in the regime of small magnetic field, low temperature, and small bias voltage, and compute the coefficients of the $\ensuremath{\sim}{B}^{2}, \ensuremath{\sim}{T}^{2}$, and $\ensuremath{\sim}{V}^{2}$ terms exactly in terms of the Fermi-liquid parameters. The coefficients of T2,V2, and B2 are found to change sign during the Kondo to empty-orbital crossover. The crossover becomes universal in the limit that the local interaction is much larger than the level width. For completeness, we also compute the shot noise and discuss the resulting Fano factor.
The appearance of unconventional superconductivity near heavy-fermion quantum critical points (QCPs) motivates investigation of pairing correlations close to a ``beyond Landau'' Kondo-destruction QCP. We focus on a two-Anderson-impurity cluster in which Kondo destruction is induced by a pseudogap in the conduction-electron density of states. Analysis via continuous-time quantum Monte Carlo and the numerical renormalization group reveals a previously unstudied QCP that both displays the critical-local moment fluctuations characteristic of Kondo destruction and leads to a strongly enhanced singlet-pairing susceptibility. Our results provide insights into the mechanism for superconductivity in quantum critical metals.
We study by Wilson numerical renormalization group the spectral properties of a two-orbital Anderson impurity model in the presence of an exchange splitting that follows either regular or inverted Hund's rules. The phase diagram contains a non-Fermi-liquid fixed point separating a screened phase, where conventional Kondo effect occurs, from an unscreened one, where the exchange splitting takes care of quenching the impurity degrees of freedom. On the Kondo screened side close to this fixed point the impurity density of states shows a narrow Kondo peak on top of a broader resonance. This narrow peak transforms in the unscreened phase into a narrow pseudogap inside the broad resonance. Right at the fixed point only the latter survives. The fixed point is therefore identified by a jump of the density of states at the chemical potential. We also consider the effect of several particle-hole symmetry-breaking terms. We show that particle-hole perturbations that simply shift the orbital energies do not wash out the fixed point, unlike those perturbations that hybridize the two orbitals. Consequently the density-of-state jump at the chemical potential remains finite even away from particle-hole symmetry. In other words, the pseudogap stays pinned at the chemical potential, although it is partially filled in. We also discuss the relevance of these results for lattice models that map onto this Anderson impurity model in the limit of large lattice coordination. Upon approaching the Mott metal-insulator transition, these lattice models necessarily enter a region with a local criticality that reflects the impurity non-Fermi-liquid fixed point. However, unlike the impurity, the lattice can get rid of the single-impurity fixed-point instability by spontaneously developing bulk coherent symmetry-broken phases, which we identify for different lattice models.