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.
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.
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.
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.
The density matrix renormalization group method is introduced in energy space to study Anderson impurity models. The method allows for calculations in the thermodynamic limit and is advantageous for studying not only the dynamical properties, but also the quantum entanglement of the ground state at the vicinity of an impurity quantum phase transition. This method is applied to obtain numerically exactly the ground-state phase diagram of the single-impurity Anderson model on the honeycomb lattice at half-filling. The calculation of local static quantities shows that the phase diagram contains two distinct phases, the local moment (LM) phase and the asymmetric strong coupling (ASC) phase, but no Kondo screening phase. These results are supported by the local spin and charge excitation spectra, which exhibit qualitatively different behavior in these two phases and also reveal the existence of the valence fluctuating point at the phase boundary. For comparison, we also study the low-energy effective pseudogap Anderson model using the method introduced here. Although the high-energy excitations are obviously different, we find that the ground-state phase diagram and the asymptotically low-energy excitations are in good quantitative agreement with those for the single-impurity Anderson model on the honeycomb lattice, thus providing a quantitative justification for the previous studies based on low-energy approximate approaches. Furthermore, we find that the lowest entanglement level is doubly degenerate for the LM phase, whereas it is singlet for the ASC phase and is accidentally threefold degenerate at the valence fluctuating point. This should be contrasted with the degeneracy of the energy spectrum because the ground state is found to be always singlet. Our results therefore clearly demonstrate that the low-lying entanglement spectrum can be used to determine with high accuracy the phase boundary of the impurity quantum phase transition.
Effect of Γ7 and Γ8 Hybridizations on Three-Channel Kondo Phase Emerging from Ho Ions
By employing a numerical renormalization group method, we analyze a seven-orbital impurity Anderson model for Ho3+ ion with ten 4f electrons. This model includes both V7 and V8, which are hybridizations between localized 4f- and conduction electrons in Γ7 and Γ8 orbitals, respectively. For the case of V7=V8 with the local Γ5 triplet ground state, we have reported the discovery of a three-channel Kondo (TCK) phase, characterized by a residual entropy of logϕ with the golden ratio ϕ=(1+5)/2. In this research, by depicting the ground-state phase diagram on the (V8,V7) plane, we attempt to unveil the effect of V7 and V8 on the emergence of the TCK phase. After performing a lot of numerical calculations, we find that the TCK phase appears in a relatively wide region on the (V8,V7) plane. The boundary curves surrounding the TCK phase are determined by the variation of the temperature dependence in entropy and the abrupt change in energy spectra. We consider that most of the phases surrounding the TCK phase are Fermi liquids, but the non-Fermi liquid two-channel Kondo phase is unexpectedly found to exist next to the TCK phase. Finally, we briefly comment on the actual material concerning the detection of the TCK phase.
We investigate a model of two Kondo impurities coupled via an Ising interaction. Exploiting the mapping to a generalized single-impurity Anderson model, we establish that the model has a singlet and a (pseudospin) doublet phase separated by a Kosterlitz-Thouless quantum phase transition. Based on a strong-coupling analysis and renormalization-group arguments, we show that at this transition the conductance G through the system either displays a zero-bias anomaly, $G\ensuremath{\sim}{\ensuremath{\mid}V\ensuremath{\mid}}^{\ensuremath{-}2(\sqrt{2}\ensuremath{-}1)}$, or takes a universal value, $G=({e}^{2}∕\ensuremath{\pi}\ensuremath{\hbar}){\mathrm{cos}}^{2}(\ensuremath{\pi}∕2\sqrt{2})$, depending on the experimental setup. Close to the Toulouse point of the individual Kondo impurities, the strong-coupling analysis allows us to obtain the location of the phase boundary analytically. For general model parameters, we determine the phase diagram and investigate the thermodynamics using numerical renormalization-group calculations. In the singlet phase close to the quantum phase transition, the entropy is quenched in two steps: first the two Ising-coupled spins form a magnetic minidomain which is, in a second step, screened by a Kondoesque collective resonance in an effective solitonic Fermi sea. In addition, we present a flow-equation analysis which provides a different mapping of the two-impurity model to a generalized single-impurity Anderson model in terms of fully renormalized couplings, which is applicable for the whole range of model parameters.
The ground state and gap properties of a spinless model of f and d electrons with hybridization V and $f\ensuremath{-}d$ interaction Ufd are studied in one dimension using a real-space renormalizationgroup (RG) method. To understand the dependence of the RG results on the cell size chosen, we first study the problem for Ufd=0 and arbitrary cell size N. It is found that even-site cells give qualitatively incorrect results for the gap, while odd-site cells (as small as N=3) reproduce very accurately the exact results for the gap and give a reasonable upper bound for the groundstate energy. On the basis of this result the phase diagram is studied as a function of arbitrary V and Ufd using three site cells. We consider the half-filled band situation for which the ground state is found to be insulating for all values of ${U}_{\mathrm{fd}}(\ensuremath{\ne}0)$. The f-electron occupation number as a function of Ef changes continuously, confirming recent mean-field results. This result indicates that the interacting $f\ensuremath{-}d$ system does not scale to a single impurity model as argued in previous studies. Using a Jordan-Wigner transformation from spin to fermion operators, the Kondo necklace model is mapped onto a fluctuating valence model and the transition from ferromagnetic to Kondo-state behavior is numerically studied using N=3.