We consider the non-Fermi liquid quantum critical state of the spin-S two-impurity Kondo model, and its potential realization in a quantum dot device. Using conformal field theory (CFT) and the numerical renormalization group (NRG), we show the critical point to be identical to that of the two-channel Kondo model with additional potential scattering, for any spin-S. Distinct conductance signatures are shown to arise as a function of device asymmetry; with the `smoking gun' square-root behavior, commonly believed to arise at low-energies, dominant only in certain regimes.
In the first step, experiments on a single cerium or ytterbium Kondo impurity reveal the importance of the Kondo temperature by comparison to other type of couplings like the hyperfine interaction, the crystal field and the intersite coupling. The extension to a lattice is discussed. Emphasis is given on the fact that the occupation number $n_f$ of the trivalent configuration may be the implicit key variable even for the Kondo lattice. Three $(P, H, T)$ phase diagrams are discussed: CeRu$_2$Si$_2$, CeRhIn$_5$ and SmS.
The single impurity Kondo model is often used to describe metals with dilute concentrations (n_i) of magnetic impurities. Here we examine how dilute the impurities must be for this to be valid by developing a virial expansion in impurity density. The O(n_i^2) term is determined from results on the 2-impurity Kondo problem by averaging over the RKKY coupling. The non-trivial fixed point of the 2-impurity problem could produce novel singularities in the heat capacity of dilute alloys at O(n_i^2).
A spin-1/2 magnetic impurity coupled to a one-dimensional correlated electron system have been studied by applying the density renormalization group method. The Kondo temperature is substantially enhanced by strong repulsive interactions in the chain, but changes non-monotonically in the case of electron attraction. The magnetization of the impurity at zero- temperature shows local Fermi liquid behavior.
We show that a self-assembled phase of potassium (K) doped single-layer para-sexiphenyl (PSP) film on gold substrate is an excellent platform for studying the two-impurity Kondo model. On K-doped PSP molecules well separated from others, we find a Kondo resonance peak near EF with a Kondo temperature of about 30 K. The Kondo resonance peak splits when another K-doped PSP molecule is present in the vicinity, and the splitting gradually increases with the decreased inter-molecular distance, with no signs of phase transition. Our data demonstrate how a Kondo singlet state gradually evolves into a…
The multichannel Kondo model supports effective anyons on the partially screened impurity, as suggested by its fractional impurity entropy. It was recently demonstrated for the multi-impurity chiral Kondo model, that scattering of an electron through the impurities depends on the anyon's total fusion channel. Here we study the correlation between impurity-spins. We argue, based on a combination of conformal field theory, a perturbative limit with a large number of channels $k$, and the exactly solvable two-channel case, that the inter-impurity spin correlation probes the anyon fusion of the pa…
We study how the formation of the Kondo compensation cloud influences the dynamical properties of a magnetic impurity that tunnels between two positions in a metal. The Kondo effect dynamically generates a strong tunneling impurity-conduction electron coupling, changes the temperature dependence of the tunneling rate, and may ultimately result in the destruction of the coherent motion of the particle at zero temperature. We find an interesting two-channel Kondo fixed point as well for a vanishing overlap between the electronic states that screen the magnetic impurity. We propose a number of sy…
We present an analytic universal impurity solver for strongly correlated electrons. We extend the many-body perturbation expansion via suitable two-particle renormalizations from the Fermi-liquid regime to the critical region of the metal-insulator transition. The reliability of the approximation in the strong-coupling limit is demonstrated by reproducing the Kondo scale in the single-impurity Anderson model. We disclose the origin of the Kondo resonance in terms of Feynman diagrams and find criteria for the existence of the proper Kondo asymptotic behavior in approximate theories.
We study the real-time dynamics of the Kondo effect after a quantum quench in which a magnetic impurity is coupled to two metallic Hubbard chains. Using an effective field theory approach, we find that for noninteracting electrons the charge current across the impurity is given by a scaling function that involves the Kondo time. In the interacting case, we show that the Kondo time decreases with the strength of the repulsive interaction and the time dependence of the current reveals signatures of the Kondo effect in a Luttinger liquid. In addition, we verify that the relaxation of the impurity…
The method of continuous unitary transformations (CUTs) is applied to the Anderson impurity and the Kondo model aiming at the systematic derivation of convergent effective models. If CUTs are applied in a conventional way, diverging differential equations occur. Similar to poor man's scaling the energy scale, below which the couplings diverge, corresponds to the Kondo temperature $T_K$. We present a way to apply CUTs to the Kondo and to the Anderson impurity model so that no divergences occur but a converged effective low-energy model is derived with small fnite parameters at arbitrarily small…
Probing Collective and Individual Kondo Screening: Multi-Stage, Multi-Channel Kondo Effects in a $C_3$-Symmetric Four-Impurity Model
Chongqing University（重庆大学）；Hangzhou Normal University（杭州师范大学）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
It is believed that the successive antiferromagnetic scattering of the conduction electrons on two magnetic impurities in a metal, induces a magnetic interaction between the impurities which sets an energy scale for the system, in addition to the Kondo temperature. However, it is shown here that this contradicts a scaling law for the two-impurity Anderson model in the magnetic limit which becomes exact for a large bandwidth.
We study the system of two magnetic impurities described by a two-impurity Kondo model where only the first impurity couples directly to the conduction band, while the second impurity interacts with the first through Heisenberg exchange coupling in a "side-coupled" configuration. We consider various choices of the impurity spins (S_1<S_2, S_1=S_2, and S_1>S_2) and we contrast the regimes where the inter-impurity exchange coupling J is either lower or higher than the Kondo temperature T_K^(0) of the first impurity in the absence of the second. This model is a high-spin generalization of the two…
We consider the spatial spin correlations around a partially screened spin-1 magnetic moment in a metal exhibiting the underscreened Kondo effect. We find that the underscreening of the impurity spin results in spatial spin correlations that are more pronounced as compared to the fully screened Kondo effect; their power-law decay is weaker because of characteristic logarithmic corrections at large distances. The spin correlator also changes sign as a function of distance to the impurity allowing for ferromagnetic correlations between conduction electron spin density and the local moment. The n…
A generalized Anderson model for a magnetic ion in a harmonic potential is formulated. The model is investigated by the numerical renormalization group(NRG) method. In addition to the conventional s-wave screening, the model exhibits phonon assisted p-wave Kondo effect as well as Yu and Anderson type Kondo effect. It is shown that the s-wave Kondo and the Yu-Anderson Kondo belong to the same fixed point. At the boundary between the s-wave and p-wave Kondo regions line of fixed points of the two channel Kondo effect is identified.
A Bethe Ansatz solution of a (modified) Hubbard chain with a Kondo impurity of arbitrary spin S at a highly symmetric line of parameter space is proposed and explored. Our results confirm the existence of a strong-coupling (line of) fixed-point(s) with ferromagnetic Kondo coupling as first hypothetized by Furusaki and Nagaosa on the basis of perturbative renormalization group calculations. For on-site Hubbard repulsion and ferromagnetic Kondo exchange, the ground state has spin S-1/2, i.e., is a singlet when S=1/2. The contributions of the impurity to the magnetic susceptibility and low-temper…
In his renormalization paper of the Kondo effect Wilson replaced the full band of s-electrons by a small number of ''Wilson states''. He started from a rather artificial symmetric band with constant density of states and constant interaction with the impurity. It is shown in the present paper that with a minor modification the Wilson states are optimally suited to treat the interaction of an impurity with an arbitrary s-band. Each Wilson state represents electrons of a whole energy range. It carries the interaction of all these electrons with the impurity. All the other electron states in this…
The Kondo resonance at the Fermi level is well-established for the electronic structure of Ce (f1 electron) and Yb (f1 hole) based systems. In this work, we report complementary experimental and theoretical studies on the Kondo resonance in Pr-based f2 system, PrTi2Al20. Using Pr 3d-4f resonant photoemission spectroscopy and single impurity Anderson model (SIAM) calculations including the full multiplets of Pr ions, we show that an f2 system can also give rise to a Kondo resonance at the Fermi level. The Kondo resonance peak is experimentally observed through a final-state-multiplet dependent …
The behavior of two magnetic impurities coupled to correlated electrons in one dimension is studied using the DMRG technique for several fillings. On-site Coulomb interactions among the electrons lead to a small Kondo screening cloud and an overall suppression of magnetic order. For arbitrary electronic correlations and large inter-impurity distances R, we find a 1/R^2 decay of magnetic correlations.
A magnetic impurity in the spin-1/2 chain is a simple realization of the two-channel Kondo problem since the field theoretical descriptions in the spin-sector are identical. The correlation functions near the impurity can be calculated. Using a modified version of the numerical transfer matrix DMRG, we are able to accurately determine local properties close to the impurity in the thermodynamic limit. The local susceptibilities (Knight-shifts) show an interesting behavior in a large range around the impurities. We are able to make quantitative experimental predictions which would allow to obser…
Accurate numerical results are derived for transport properties of Kondo impurity systems with potential scattering and orbital degeneracy. Using the continuous-time quantum Monte Carlo (CT-QMC) method, static and dynamic physical quantities are derived in a wide temperature range across the Kondo temperature T_K. With strong potential scattering, the resistivity tends to decrease with decreasing temperature, in contrast to the ordinary Kondo effect. Correspondingly, the quasi-particle density of states obtains the antiresonance around the Fermi level. Thermopower also shows characteristic dev…
We use two different methods, the Hirsch-Fye quantum Monte Carlo simulation and the slave-boson mean field analysis to estimate the effect of spin-orbit coupling on the Kondo temperature in a quantum wire. In quantum Monte Carlo simulation, we calculate the product of spin susceptibility and temperature for different spin-orbit couplings and impurity energies. The variation of the Kondo temperature is estimated via the low temperature universal curves. In the mean field analysis, the Kondo temperature is estimated as the condensation temperature of slave-boson. Both the two methods demonstrate…
A recently developed continuous time solver based on an expansion in hybridization about an exactly solved local limit is reformulated in a manner appropriate for general classes of quantum impurity models including spin exchange and pair hopping terms. The utility of the approach is demonstrated via applications to the dynamical mean field theory of the Kondo lattice and two-orbital models. The algorithm can handle low temperatures and strong couplings without encountering a sign problem.
In a Kondo lattice, the spin exchange coupling between a local spin and the conduction electrons acquires nonlocal contributions due to conduction electron scattering from surrounding local spins and the subsequent RKKY interaction. It leads to a hitherto unrecognized interference of Kondo screening and the RKKY interaction beyond the Doniach scenario. We develop a renormalization group theory for the RKKY-modified Kondo vertex. The Kondo temperature, $T_K(y)$, is suppressed in a universal way, controlled by the antiferromagnetic RKKY coupling parameter $y$. Complete spin screening ceases to e…
We study the Kondo screening of a magnetic impurity in a two-dimensional superconductor with Rashba spin-orbit coupling (SOC). It is found that the Rashba interaction generates a novel Kondo screening channel, in which the local moment is screened by the exchange coupling with conduction electrons in different spin and orbital states. The Kondo temperature associated with this process is determined by the interplay between the Rashba SOC and superconducting energy gap. As a result, the quantum phase transition between the magnetic doublet and Kondo singlet ground states is significantly affect…
A magnetic moment in a metal or in a quantum dot is, at low temperatures, screened by the conduction electrons through the mechanism of the Kondo effect. This gives rise to spin-spin correlations between the magnetic moment and the conduction electrons, which can have a substantial spatial extension. We study this phenomenon, the so-called Kondo cloud, by means of the density matrix renormalization group method for the case of the single-impurity Anderson model. We focus on the question whether the Kondo screening length, typically assumed to be proportional to the inverse Kondo temperature, c…
In the present paper, we present an efficient continuous-time quantum Monte Carlo impurity solver with high acceptance rate at low temperature for multi-orbital quantum impurity models with general interaction. In this hybridization expansion impurity solver, the imaginary time evolution operator for the high energy multiplets, which decays very rapidly with the imaginary time, is approximated by a probability normalized $δ$-function. As the result, the virtual charge fluctuations of $f^{n}\rightarrow f^{n\pm1}$ are well included on the same footing without applying Schrieffer-Wolff transforma…
Motivated by recent STM experiments, we explore the magnetic field induced Kondo effect that takes place at symmetry protected level crossings in finite Co adatom chains. We argue that the effective two-level system realized at a level crossing acts as an extended impurity coupled to the conduction electrons of the substrate by a distribution of Kondo couplings at the sites of the chain. Using auxiliary-field quantum Monte Carlo simulations, which quantitatively reproduce the field dependence of the zero-bias signal, we show that a proper Kondo resonance is present at the sites where the effec…
We study a generalization of the Kondo model in which the impurity spin is represented by Abrikosov fermions in a rotation group SU(P) larger than the SU(N) group associated to the spin of the conduction electrons, thereby forcing the single electronic bath to underscreen the localized moment. We demonstrate how to formulate a controlled large N limit preserving the property of underscreening, and which can be seen as a ``dual'' theory of the multichannel large N equations usually associated to overscreening. Due to the anomalous scattering on the uncompensated degrees of freedom, the Fermi li…
We investigate how Kondo phenomenon occurs in the Anderson model dynamically coupled with local Jahn-Teller phonons. It is found that the total angular moment composed of electron pseudo-spin and phonon angular moments is screened by conduction electrons. Namely, phonon degrees of freedom essentially contribute to the formation of singlet ground state. A characteristic temperature of the Kondo effect due to dynamical Jahn-Teller phonons is explained by an effective $s$-$d$ Hamiltonian with anisotropic exchange interaction obtained from the Jahn-Teller-Anderson model in a non-adiabatic region.
The conduction electron density of states nearby single magnetic impurities, as measured recently by scanning tunneling microscopy (STM), is calculated, taking into account tunneling into conduction electron states only. The Kondo effect induces a narrow Fano resonance in the conduction electron density of states, while scattering off the d-level generates a weakly energy dependent Friedel oscillation. The line shape varies with the distance between STM tip and impurity, in qualitative agreement with experiments, but is very sensitive to details of the band structure. For a Co impurity the exp…
The periodic Anderson impurity model on the Lieb lattice is studied by the slave-boson mean-field approximation in the strong interaction limit. The electron structure of conduction electrons on the Lieb lattice features both the band flatness and soft gap at low energy. With these features conduction electrons can form both the soft-gap and the molecular Kondo singlets with the magnetic impurities, and this leads to a competition between the soft-gap and the molecular Kondo effects in the lattice. We find a selective Kondo strong coupling, where at selected sites the magnetic impurities are s…
We show through a perturbative and an exact calculation using Wilson's renormalization methods that in the problem of two interacting Kondo impurities, on-site potential scattering generates a quantum-tunneling between the two impurities through a marginally relevant operator. The magnitude of this tunneling $V_{12}$ depends on the spin-correlation between the two impurities. For exchange interactions between the moments comparable to the Kondo energy $T_K$, $V_{12}$ is typically much larger than $T_K$. This implies that the heavy-fermion mass in this interesting range is determined by $V_{12}…
The underscreened Kondo effect is studied within a model of two impurities S=1 interacting with the conduction band and via an interimpurity coupling $K\vec{S_1}.\vec{S_2}$. Using a mean-field treatment of the bosonized Hamiltonian, we show that there is no phase transition, but a continuous cross-over versus K from a non Kondo behaviour to an underscreened Kondo one. For a small antiferromagnetic coupling (K>0), a completely asymmetric situation is obtained with one s=${1/2}$ component strongly screened by the Kondo effect and the other one almost free to yield indirect magnetism, which shows…
The existence of a length-scale $ξ_K\sim 1/T_K$ (with $T_K$ the Kondo temperature) has long been predicted in quantum impurity systems. At low temperatures $T\ll T_K$, the standard interpretation is that a spin-$\tfrac{1}{2}$ impurity is screened by a surrounding `Kondo cloud' of spatial extent $ξ_K$. We argue that renormalization group (RG) flow between any two fixed points (FPs) results in a characteristic length-scale, observed in real-space as a crossover between physical behaviour typical of each FP. In the simplest example of the Anderson impurity model, three FPs arise; and we show that…
We study the fate of a spin-1/2 impurity in the itinerant antiferromagnetic metallic phase via a renormalization group analysis and a variational calculation. The local moment - conduction electron interaction hamiltonian in an antiferromagnetic metal is spin non-conserving. We show that for a general location of the impurity, the Kondo singularities still occur, but the ground state has a partially unscreened moment. We calculate the magnitude of this residual moment and the variation of the spin polarization with energy for a substitutional impurity as a function of the staggered magnetizati…
Two magnetic atoms, one attached to the tip of a Scanning Tunneling Microscope (STM) and one adsorbed on a metal surface, each constituting a Kondo system, have been proposed as one of the simplest conceivable systems potentially exhibiting quantum critical behaviour. We have succeeded in implementing this concept experimentally for cobalt dimers clamped between an STM tip and a gold surface. Control of the tip-sample distance with sub-picometer resolution allows us to tune the interaction between the two cobalt atoms with unprecedented precision. Electronic transport measurements on this two-…
A magnetic impurity embedded in a metal host is collectively screened by a cloud of conduction electrons to form a Kondo singlet below a characteristic energy scale $T_K$, the Kondo temperature, through the mechanism of the Kondo effect. We have reinvestigated the Kondo singlet by means of the newly developed natural orbitals renormalization group (NORG) method. We find that, in the framework of natural orbitals formalism, the Kondo screening mechanism becomes transparent and simple, while the intrinsic structure of Kondo singlet is clearly resolved. For a single impurity Kondo system, there e…
We have studied the ferromagnetic Kondo lattice model (FKLM) with an Anderson impurity on finite chains with numerical techniques. We are particularly interested in the metallic ferromagnetic phase of the FKLM. This model could describe either a quantum dot coupled to one-dimensional ferromagnetic leads made with manganites or a substitutional transition metal impurity in a MnO chain. We determined the region in parameter space where the impurity is empty, half-filled or doubly-occupied and hence where it is magnetic or nonmagnetic. The most important result is that we found, for a wide range …
The renormalization group formalism was applied to calculate the spin-lattice relaxation rate of a well-defined magnetic moment in the neighborhood of a spin degenerate Anderson impurity. In the Kondo regime, the spin-lattice relaxation rate as a function of the temperature presents a peak at the Kondo temperature; for temperature much lower then the Kondo temperature, the system behaves as a heavy Fermy liquid, with an enhanced density of states, which increases with the decreasing of the Kondo temperature; the product of the temperature by the relaxation rate remains an universal function of…
Temperature dependencies of the impurity magnetic susceptibility, entropy, and heat capacity have been obtained by the method of numerical renormalization group and exact diagonalization for the Kondo model with peaks in the electron density of states near the Fermi energy (in particular, with logarithmic Van Hove singularities). It is shown that these quantities can be {\it negative}. A new effect has been predicted (which, in principle, can be observed experimentally), namely, the decrease in the magnetic susceptibility and heat capacity of a nonmagnetic sample upon the addition of magnetic …
We develop a general Bethe Ansatz formalism for diagonalizing an integrable model of a magnetic impurity of arbitrary spin coupled ferro- or antiferromagnetically to a chain of interacting electrons. The method is applied to an open chain, with the exact solution revealing a ``hidden'' Kondo effect driven by forward electron scattering off the impurity. We argue that the so-called ``operator reflection matrices'' proposed in recent Bethe Ansatz studies of related models emulate only forward electron-impurity scattering which may explain the absence of complete Kondo screening for certain value…
The problem of two magnetic impurities in a normal metal exposes the two opposite tendencies in the formation of a singlet ground state, driven respectively by the single-ion Kondo effect with conduction electrons to screen impurity spins or the Ruderman-Kittel-Kasuya-Yosida interaction between the two impurities to directly form impurity spin singlet. However, whether the competition between these two tendencies can lead to a quantum critical point has been debated over more than two decades. Here, we study this problem by applying the newly proposed natural orbitals renormalization group met…
We study the low-temperature properties of the generalized Anderson impurity model in which two localized configurations, one with two doublets and the other with a triplet, are mixed by two degenerate conduction channels. By using the numerical renormalization group and the non-crossing approximation, we analyze the impurity entropy, its spectral density, and the equilibrium conductance for several values of the model parameters. Marked differences with respect to the conventional one-channel spin $s=1/2$ Anderson model, that can be traced as hallmarks of an impurity spin $S=1$, are found in …
Competition between the Kondo effect and Ruderman-Kittel-Kasuya-Yosida interaction in the two-impurity Kondo problem can be phenomenologically described by the Rasul-Schlottmann spin model. We revisit this model from the quantum entanglement perspective by calculating both the inter-impurity entanglement and the local Kondo entanglement, the latter being the entanglement between a local magnetic impurity and its spatially nearby conduction electron. A groundstate phase diagram is derived and a discontinuous breakdown of the local Kondo entanglement is found at the singular point, associated co…
Using the natural orbitals renormalization group, we studied the problem of a localized spin- 1/2 impurity coupled to two helical liquids via the Kondo interaction in a quantum spin Hall insulator, based on the Kane-Mele model defined in a finite zigzag graphene nanoribbon. We investigated the influence of the Kondo couplings with the helical liquids on both the static and dynamic properties of the ground state. The number and distinct spatial structures of the active natural orbitals (ANOs), which play essential roles in constructing the ground-state wave function, were first analyzed. Our nu…
We calculate the dynamical spin response of Kondo impurity and Kondo lattice systems within a semiphenomenological Fermi liquid description, at low temperatures $T<T_K$, the Kondo temperature, and low magnetic fields $B \ll k_B T_K/gμ_B$. Fermi liquid parameters are determined by comparison (i) with microscopic theory (numerical renormalization group) for the impurity model and (ii) with experiment for the lattice model. We find in the impurity case that the true impurity spin resonance has a width of the order of $T_K$ and disappears altogether if the $g$-factors of impurity spin and conducti…
The multipolar Kondo problem, wherein the quantum impurity carries higher-rank multipolar moments, has seen recent theoretical and experimental interest due to proposals of novel non-Fermi liquid states and the availability of a variety of material platforms. The multipolar nature of local moments, in conjunction with constraining crystal field symmetries, leads to a vast array of possible interactions and resulting non-Fermi liquid ground states. Previous works on Kondo physics have typically focussed on impurities that have two degenerate internal states. In this work, inspired by recent exp…
Using NRG, we show that a system containing a quantum impurity (QI), strongly coupled to a semiconductor (gap $2 Δ$) and weakly coupled to a metal, displays a 'reentrant' Kondo stage at low temperatures. The NRG analysis of the corresponding Single Impurity Anderson Model (SIAM) shows that the reentrant stage is characterized by a second sequence of SIAM fixed points: free orbital (FO) > local moment (LM) > strong coupling (SC). In the first stage, the SC fixed point (Kondo temperature $T_{K1}$) is unstable, while the second stage exhibits a much lower Kondo temperature $T_{K2}$, associated to…
Symmetry-breaking perturbations destabilize the critical points of the two-channel and two-impurity Kondo models, thereby leading to a crossover from non-Fermi liquid behavior to standard Fermi liquid physics. Here we use an analogy between this crossover and one occurring in the boundary Ising model to calculate the full zero temperature crossover Green function analytically. In remarkable agreement with our numerical renormalization group calculations, the single exact function applies for an arbitrary mixture of the relevant perturbations in each model. This rich behavior resulting from fin…
We investigate a quantum dot (Anderson impurity) coupled to metallic leads, with a time-periodic voltage bias across the device. Using a time-dependent Schrieffer-Wolff transformation, we show that the Floquet Hamiltonian of the model can be mapped onto a two-channel Kondo model, in which the impurity is screened by separate conduction bands corresponding to parity-even and odd superpositions of the metallic leads. By changing the frequency and amplitude of the perturbation, one can tune the system to a quantum critical point with symmetric coupling of the impurity to both channels. For the un…
Properties of a nonmagnetic impurity in Kondo insulators are investigated by considering a one-dimensional Kondo lattice model with depletion of a localized spin. The ground-state phase diagram determined by the Lanczos method shows that the magnetic moment is more stable than in ordinary metals. Temperature dependence of impurity susceptibilities is also studied by using the finite-temperature density-matrix renormalization group.
We analyze the consequences of a first-order (in the effective Kondo coupling) inter-impurity correlation present in the Two-Impurity Anderson Hamiltonian. This correlation generates a pair of Kondo Doublet states which are responsible for the first (higher energy) Kondo stage of these systems. Applied to systems of quantum dots in a semiconductor heterolayer, these Doublets predict a mainly ferromagnetic dot-dot spin correlation which is different than the expected from the second-order RKKY interaction. In order to effectively screen both dots, a parallel alignment of the dot-spins is favore…
A particle-hole symmetric Anderson impurity model with a metallic host of narrow bandwidth is studied within the framework of the local moment approach. The resultant single-particle spectra are compared to unrestricted Hartree-Fock, second order perturbation theory about the noninteracting limit, and Lanczos spectra by Hofstetter and Kehrein. Rather accurate analytical results explain the spectral evolution over almost the entire range of interactions. These encompass, in particular, a rationale for the four-peak structure observed in the low-energy sector of the Lanczos spectra in the modera…
We have performed first-principles calculation of the surface and bulk wavefunctions of the Cu(111) surface and their hybridization energies to a Co adatom, including the potential scattering from the Co. By analyzing the calculated hybridization energies, we found the bulk states dominate the contribution to the Kondo temperature, in agreement with recent experiments. Furthermore, we also calculate the tunneling conductance of a scanning tunneling microscope (STM) and compare our results with recent experiments of Co impurities in the Cu(111) surface. Good quantitative agreement is found at s…
We investigate the equilibrium and real-time properties of the spin correlation function $\langle \vec{S}_1\vec{S}_2 \rangle$ in the two-impurity Kondo model for different distances $R$ between the two-impurity spins. It is shown that the competition between the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction and the Kondo effect governs the amplitude of $\langle \vec{S}_1\vec{S}_2 \rangle$. For distances $R$ exceeding the Kondo length scale, the Kondo effect also has a profound effect on the sign of the correlation function. For ferromagnetic Heisenberg couplings $J$ between the impurities a…
Simple scaling consideration and NRG solution of the one- and two-channel Kondo model in the presence of a logarithmic Van Hove singularity at the Fermi level is given. The temperature dependences of local and impurity magnetic susceptibility and impurity entropy are calculated. The low-temperature behavior of the impurity susceptibility and impurity entropy turns out to be non-universal in the Kondo sense and independent of the $s-d$ coupling $J$. The resonant level model solution in the strong coupling regime confirms the NRG results. In the two-channel case the local susceptibility demonstr…
