Although the Kondo effect and the Kondo ground state of a magnetic impurity have been investigated for more than forty years it was until recently difficult if not impossible to calculate spatial properties of the ground state. In particular the calculation of the spatial distribution of the so-called Kondo cloud or even its existence have been elusive. In recent years a new method has been introduced to investigate the properties of magnetic impurities, the FAIR method, where the abbreviation stands for Friedel Artificially Inserted Resonance. The FAIR solution of the Friedel-Anderson and the Kondo impurity problems consists of only eight or four Slater states. Because of its compactness the spatial electron density and polarization can be easily calculated. In this article a short review of the method is given. A comparison with results from the large N-approximation, the Numerical Renormalization Group theory and other methods shows excellent agreement. The FAIR solution yields (for the first time) the electronic polarization in the Kondo cloud.
Recently Affleck et al. derived the existence of Friedel oscillations in the presence of a Kondo impurity. They supported their analytic derivation by numerical calculations using Wilson's renormalization approach (NRG). In this paper the size of the Friedel oscillations is calculated with the FAIR method (Friedel Artificially Inserted Resonance) which has been recently developed. The results of NRG and FAIR are compared. The development of Friedel oscillations with a phase shift of pi/2 outside of the Kondo radius is confirmed.
It is shown that the calculation of the magnetic moment of a Friedel-Anderson impurity in mean-field theory is unreliable. A class of approximate solutions, which contains the mean-field solution as an element, is expressed in rotated Hilbert space and optimized. The optimal state has considerably lower energy than the mean field solution and requires almost twice the Coulomb exchange U to become magnetic. Since most moment calculations of magnetic impurities, for example the spin-density-functional theory, use the mean-field approximation the resulting magnetic moments have to be critically r…
The Friedel oscillations in the vicinity of a Friedel-Anderson (FA) impurity are investigated numerically. For an FA impurity in the local moment limit the normalized amplitude A(ξ) is S-shaped, approximately zero at short distances, approaching two at large distances and crossing the value one at the characteristic length ξ_{1/2}. Surprisingly, the Friedel oscillations of a simple non-interacting Friedel impurity with a narrow resonance at the Fermi level show a very similar behavior of their amplitude A(ξ). A comparison correlates the resonance width and the Kondo energy of the FA impurity w…
By applying a magnetic field whose Zeeman energy exceeds the Kondo energy by an order of magnitude the ground state of the Friedel-Anderson impurity is a magnetic state. In recent years the author introduced the Friedel Artificially Inserted Resonance (FAIR) method to investigate impurity properties. Within this FAIR approach the magnetic ground state is derived. Its full excitation spectrum and the composition of the excitations is calculated and numerically evaluated. From the excitation spectrum the electron density of states is calculated. Majority and minority d-resonances are obtained. T…
We show that the long distance charge density oscillations in a metal induced by a weakly coupled spin-1/2 magnetic impurity exhibiting the Kondo effect are given, at zero temperature, by a universal function F(r/xi_K) where r is the distance from the impurity and xi_K, the Kondo screening cloud size =v_F/T_K, where v_F is the Fermi velocity and T_K is the Kondo temperature. F is given by a Fourier-like transform of the T-matrix. Analytic expressions for F(r/xi_K) are derived in both limits r much less than xi_K and r much greater than xi_K and F is calculated for all r/xi_K using numerical me…
The fidelities of the Kondo and the Friedel-Anderson (FA) impurities are calculated numerically. The ground states of both systems are calculated with the FAIR (Friedel artificially inserted resonance) theory. The ground state in the interacting systems is compared with a nullstate in which the interaction is zero. The different multi-electron states are expressed in terms of Wilson states. The use of N Wilson states simulates the use of a large effective number N_{eff} of states. A plot of ln(F) versus N\proptoln(N_{eff}) reveals whether one has an Anderson orthogonality catastrophe at zero e…
We address three issues on the role of magnetic impurities in the surface state of a three dimensional topological insulator. First, we prove that the Kondo effect of the topological surface is essentially the same as that of the graphene surface, demonstrating that an effective impurity action of the topological surface coincides with that of the graphene surface. Second, we study the role of the $z$-directional magnetic field ($h$) in the Kondo effect, and show that the peak splitting in the impurity local density of states does not follow the $h$-linear behavior, the typical physics in the …
We consider a magnetic impurity deposited on the surface of a strong topological insulator and interacting with the surface modes by a Kondo exchange interaction. Taking into account the warping of the Fermi line of the surface modes, we derive a mapping to an effective one dimensional model and show that the impurity is fully screened by the surface electrons except when the Fermi level lies exactly at the Dirac point. Using an Abrikosov fermion mean-field theory, we calculate the shape of the electronic density Friedel oscillation resulting from the presence of the Kondo screening cloud. We …
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…
We reobtain the Kondo-Doublet interaction by means of the Brillouin-Wigner Perturbation theory. By applying the same method to the single impurity case we show that the Kondo-Doublet interaction is a direct consequence of the Kondo screening cloud. We fully confirm our previous results on this novel interaction. In particular, we found that for values of the system parameters typical of semiconductor Quantum Dots heterostructures, the ferromagnetic Kondo-Doublet interaction dominates over the RKKY one.
We analyze two pairs of doublet states for the two Anderson impurity problem. We found that for short interimpurity distances they have a lower energy than the ferro triplet and the antiferro singlet. For medium to long distances between the impurities, the doublets also have a lower energy than the two decoupled Kondo-singlet state for most of the range of interest. The mechanism behind their energy gain is an coherence enhanced Kondo-like interaction.
We analyze the effects of high energy configurations on the Kondo-doublet interaction between two Anderson impurities. We found that the Kondo doublet states are robust and that their coherence energy is incremented by the inclusion of high energy configurations. Analytic expressions are obtained for the corrections near the Kondo limit. Analysis of the system in the intermediate valence regime shows that the behavior of the system can be changed from ferromagnetic to sligthy antiferromagnetic by tuning the system parameters; this regime can also be used to study the interplay between hole-dri…
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…
One of the great achievements performed by Jacques Friedel in France has been to promote experimental activities on the electronic properties in condensed matter physics, which has led him, among others, to be an active promoter of the up-rise of the "Laboratoire de Physique des Solides" (LPS). A selective presentation of some of the work achieved in my Nuclear Magnetic Resonance (NMR) group allows me to underline the importance of the initial choices done by J. Friedel for the LPS. I give here an updated review of the work done on Kondo effect in the 1970's which has allowed me to enlighten t…
We investigate the dynamical and steady-state spin response of the nonequilibrium Anderson model to magnetic fields, bias voltage, and temperature using a numerically exact method combining a bold-line quantum Monte Carlo technique with the memory function formalism. We obtain converged results in a range of previously inaccessible regimes, in particular the crossover to the Kondo domain. We provide detailed predictions for novel nonequilibrium phenomena, including non-monotonic temperature dependence of observables at high bias voltage and oscillatory quench dynamics at high magnetic fields.
The internal s-electron polarization in the ground state of a Friedel-Anderson and a Kondo impurity is calculated. The Wilson basis with exponentially fine energies close to the Fermi level is used and expressed in terms of free electron waves with linear energy-momentum dispersion. It is found that in the singlet state the magnetic moment of the d-electron is screened by an s-electron cloud. The linear extension of the cloud is inversely proportional to the Kondo energy. When the singlet state is destroyed the polarization cloud is absent.
The Distributional Exact Diagonalization (DED) scheme is applied to the description of Kondo physics in the Anderson impurity model. DED maps Anderson's problem of an interacting impurity level coupled to an infinite bath onto an ensemble of finite Anderson models, each of which can be solved by exact diagonalization. An approximation to the self-energy of the original infinite model is then obtained from the ensemble averaged self-energy. Using Friedel's sum rule, we show that the particle number constraint, a central ingredient of the DED scheme, ultimately imposes Fermi liquid behavior on t…
In the presence of a magnetic impurity the spin-up and down band states are modified differently by the impurity. If the multi-electron scalar product (MESP) between the occupied spin-up and down states approaches zero then this defines an orthogonality catastrophe. In the present paper the MESP is investigated for the FAIR (Friedel Artificial Iserted Resonance) solution for a Friedel-Anderson impurity. A basis of Wilson states is used. The MESP is numerically determined for the (enforced) magnetic, the singlet, and the triplet states as a function of the number N of Wilson states. The magneti…
Nonlinear tunneling current through a quantum dot (an Anderson impurity system) subject to both constant and alternating electric fields is studied in the Kondo regime. A systematic diagram technique is developed for perturbation study of the current in physical systems out of equilibrium governed by time - dependent Hamiltonians of the Anderson and the Kondo models. The ensuing calculations prove to be too complicated for the Anderson model, and hence, a mapping on an effective Kondo problem is called for. This is achieved by constructing a time - dependent version of the Schrieffer - Wolff t…
The concept of dynamical symmetries is used for formulation of the renormalization group approach to the Kondo effect in the Anderson model with repulsive and attractive interaction $U$. It is shown that the generic local symmetry of the Anderson Hamiltonian is determined by the SU(4) Lie group. The Anderson Hamiltonian is rewritten in terms of the Gell-Mann matrices of the 4-th rank, which form the set of group generators and the basis for construction of irreducible vector operators describing the excitation spectra in the charge and spin sectors. The multistage Kondo sceening is described i…
The Kondo effect in quantum dots (QDs) - artificial magnetic impurities - attached to ferromagnetic leads is studied with the numerical renormalization group (NRG) method. It is shown that the QD level is spin-split due to presence of ferromagnetic electrodes, leading to a suppression of the Kondo effect. We find that the Kondo effect can be restored by compensating this splitting with a magnetic field. Although the resulting Kondo resonance then has an unusual spin asymmetry with a reduced Kondo temperature, the ground state is still a locally-screened state, describable by Fermi liquid theor…
We investigate Kondo correlations in a quantum dot with normal and superconducting electrodes, where a spin bias voltage is applied across the device and the local interaction $U$ is either attractive or repulsive. When the spin current is blockaded in the large-gap regime, this nonequilibrium strongly-correlated problem maps into an equilibrium model solvable by the numerical renormalization group method. The Kondo spectra with characteristic splitting due to the nonequilibrium spin accumulation are thus obtained at high precision. It is shown that while the bias-induced decoherence of the sp…
We analyze the two Anderson impurity problem, in the strong Coulomb repulsion limit, by means of variational wave functions whose equations we solve analytically. We found two pairs of Doublet states, one odd and one even with respect to the midplane between the impurities. These Doublets make a significatively strong use of the hybridization terms of the Hamiltonian, and have a much larger Kondo-like correlation energy than a single impurity (the Kondo energy). Furthermore, these Doublets combine to form a Super-Singlet. This Super-Singlet makes use of the remaining hybridization probability …
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…
It is shown that the Kondo lattice model, for any finite coupling constant J, can be obtained exactly from the periodic Anderson model in an appropriate limit. The mapping allows a direct proof of the 'large' Fermi volume for a nonmagnetic Fermi-liquid state of the Kondo lattice model.
We argue that the Anderson and Kondo models turn out to be irrelevant for the description of some strongly correlated electron systems and we suggest the mechanism for the formation of many-body states (heavy fermions) being an alternative to the Kondo one. This mechanism involves the quantum tunneling of a heavy particle between the states in the double-well potential.
We show that an Anderson Hamiltonian describing a quantum dot connected to multiple leads is integrable. A general expression for the non-linear conductance is obtained by combining the Bethe ansatz exact solution with Landauer-Büttiker theory. In the Kondo regime, a closed form expression is given for the matrix conductance at zero temperature and when all the leads are close to the symmetric point. A bias-induced splitting of the Kondo resonance is possible for three or more leads. Specifically, for $N$ leads, with each at a different chemical potential, there can be $N-1$ Kondo peaks in the…
We investigate a modified Anderson model at the large-$N$ limit, where Coulomb interaction is replaced by Sachdev-Ye-Kitaev random interaction. The resistivity of conduction electron $ρ_{c}$ has a minimum value around temperature $\widetilde{T}_{K}$, which is similar to the Kondo system, but the impurity electron's density of state $A_{d}(ω)$ elucidates no sharp-peak like Kondo resonance around the Fermi surface. The impurity electron's entropy $S_{d}$ and specific heat capacity $C_{\textrm{v}}$ illustrate a crossover from Fermi liquid to the non-Fermi liquid. The system is a non-Fermi liquid …
The system of several (N) quantum dots coupled in parallel to the same single-mode conduction channel can be modelled as a single-channel N-impurity Anderson model. Using the generalized Schrieffer-Wolff transformation we show that near the particle-hole symmetric point, the effective Hamiltonian in the local moment regime is the N-impurity S=1/2 Kondo model. The conduction-band-mediated RKKY exchange interaction between the dots is ferromagnetic and at intermediate temperatures locks the moments into a maximal spin S=N/2 ground state. We provide an analytical estimate for the RKKY interaction…
We calculate conductance through a quantum dot weakly coupled to metallic contacts by means of Keldysh out of equilibrium formalism. We model the quantum dot with the SU(2) Anderson model and consider the limit of infinite Coulomb repulsion. We solve the interacting system with the numerical diagrammatic Non-Crossing Approximation (NCA). We calculate the conductance as a function of temperature and gate voltage, from differential conductance (dI/dV) curves. We discuss these results in comparison with those from the linear response approach which can be performed directly in equilibrium conditi…
We demonstrate that the conductance through a single-electron transistor at low temperature is in quantitative agreement with predictions of the equilibrium Anderson model. When an unpaired electron is localized within the transistor, the Kondo effect is observed. Tuning the unpaired electron's energy toward the Fermi level in nearby leads produces a cross-over between the Kondo and mixed-valence regimes of the Anderson model.
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…
The localization length, $ξ$, in a 2--dimensional Anderson insulator depends on the electron spin scattering rate by magnetic impurities, $τ_s^{-1}$. For antiferromagnetic sign of the exchange, %constant, the time $τ_s$ is {\em itself a function of $ξ$}, due to the Kondo correlations. We demonstrate that the unitary regime of localization is impossible when the concentration of magnetic impurities, $n_{\tiny M}$, is smaller than a critical value, $n_c$. For $n_{\tiny M}>n_c$, the dependence of $ξ$ on the dimensionless conductance, $g$, is {\em reentrant}, crossing over to unitary, and back to …
The periodic Anderson model is extended by switching on a Hubbard U for the conduction electrons. We use the Gutzwiller variational method to study the nearly integral valent limit. The lattice Kondo energy contains the U-dependent chemical potential of the Hubbard subsystem in the exponent, and the correlation-induced band narrowing in the prefactor. Both effects tend to suppress the Kondo scale, which can be understood to result from the blocking of hybridization. At half-filling, we find a Brinkman-Rice-type transition from a Kondo insulator to a Mott insulator.
In the present work we apply the atomic approach to the single impurity Anderson model (SIAM). A general formulation of this approach, that can be applied both to the impurity and to the lattice Anderson Hamiltonian, was developed in a previous work (arXiv:0903.0139v1 [cond-mat.str-el]). The method starts from the cumulant expansion of the periodic Anderson model (PAM), employing the hybridization as perturbation. The atomic Anderson limit is analytically solved and its sixteen eigenenergies and eigenstates are obtained. This atomic Anderson solution, which we call the (AAS), has all the funda…
Linear conductance through a quantum dot is calculated under a finite magnetic field using the modified perturbation theory. The method is based on the second-order perturbation theory with respect to the Coulomb repulsion, but the self-energy is modified to reproduce the correct atomic limit and to fulfill the Friedel sum rule exactly. Although this method is applicable only to zero temperature in a strict sense, it is approximately extended to finite temperatures. It is found that the conductance near electron-hole symmetry is suppressed by the application of the magnetic field at low temper…
We show within the slave boson technique, that the Anderson lattice model exhibits a Kondo breakdown quantum critical point (KB-QCP) where the hybridization goes to zero at zero temper- ature. At this fixed point, the f-electrons experience as well a selective Mott transition separating a local-moment phase from a Kondo-screened phase. The presence of a multi-scale QCP in the An- derson lattice in the absence of magnetism is discussed in the context of heavy fermion compounds. This study is the first evidence for a selective Mott transition in the Anderson lattice.
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 effect of binary alloy disorder on the ferromagnetic phases of f-electron materials is studied within the periodic Anderson model. We find that disorder in the conduction band can drastically enhance the Curie temperature due to an increase of the local f-moment. The effect may be explained qualitatively and even quantitatively by a simple theoretical ansatz. The emergence of an alloy Kondo insulator at non-integer filling is also pointed out.
The thermodynamics of a lattice regularized asymmetric Anderson impurity in a correlated host is obtained by an exact solution. The crossover from the Anderson- to the Kondo-regime is studied, thus making contact with predictions by scaling theory. On the basis of the exact solution, the transition to universal Kondo behavior is shown to be realized by a graduate separation of the energy scales of spin and charge excitations.
The low-temperature behavior of the asymmetric single-impurity Anderson model is studied by diagrammatic methods resulting in analytically controllable approximations. We first discuss the ways one can simplify parquet equations in critical regions of singularities in the two-particle vertex. The scale vanishing at the critical point defines the Kondo temperature at which the electron-hole correlation function saturates. We show that the Kondo temperature exists at any filling of the impurity level. A quasiparticle resonance peak in the spectral function, however, forms only in almost electron…
The influence of spin-orbit interactions on the Kondo effect has been under debate recently. Studies conducted recently on a system composed by an Anderson impurity on a 2DEG with Rashba spin-orbit have been shown that it can enhance or suppress the Kondo temperature ($T_{\rm K}$), depending on the relative energy level position of the impurity with respect to the particle-hole symmetric point. Here we investigate a system composed by a single Anderson impurity side-coupled to a quantum wire with spin-orbit coupling (SOC). We derive an effective Hamiltonian in which the Kondo coupling is modif…
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…
We study a localized spin coupled to an Anderson impurity to model the situation found in higher transition metal or rare earth compounds like e.g.\ LaMnO$_3$ or Gd monopnictides. We find that, even for large quantum numbers of the localized spin, quantum fluctuations play an essential role for the case of ferromagnetic coupling between the spin and the impurity levels. For antiferromagnetic coupling, a description in terms of a classical spin is appropriate.
The present work is based on the nonequilibrium perturbative formalism. There the self-energies are derived up to the forth-order. In consequence, it proves that the nonequilibrium (real-time) perturbative expansion can be connected with the Matsubara imaginary-time perturbative expansion for equilibrium. As the numerical results, the Kondo resonance still disappears for bias voltage exceeding the Kondo temperatures, as observed in experiments of two terminal systems.
The nonequilibrium time evolution of a quantum dot is studied by means of dynamic equations for time-dependent Greens functions derived from a two-particle-irreducible (2PI) effective action for the Anderson impurity model. Coupling the dot between two leads at different voltages, the dynamics of the current through the dot is investigated. We show that the 2PI approach is capable to describe the dynamical build-up of the Kondo effect, which shows up as a sharp resonance in the spectral function, with a width exponentially suppressed in the electron self coupling on the dot. An external voltag…
Metallic quantum criticality often develops in strongly correlated systems with local effective degrees of freedom. In this work, we consider an Anderson lattice model with SU(2) symmetry. The model is treated by the extended dynamical mean-field theory (EDMFT) in combination with a continuous-time quantum Monte Carlo method. We demonstrate a continuous quantum phase transition, establish the ensuing quantum critical point to be of a Kondo-destruction type, and determine the anomalous scaling properties. We connect the continuous nature of the transition to a dynamical Kondo effect, which we c…
We investigate the paramagnetic periodic Anderson model using the dynamical mean-field theory in combination with the modified perturbation theory which interpolates between the weak and strong coupling limits. For the symmetric PAM, the ground state is always a singlet state. However, as function of the hybridization strength, a crossover from collective to local Kondo screening is found. Reducing the number of conduction electrons, the local Kondo singlets remain stable. The unpaired f-electrons dominate the physics of the system. For very low conduction electron densities, a large increase …
The variational cluster approach (VCA) based on the self-energy functional theory is applied to the two-dimensional symmetric periodic Anderson model at half filling. We calculate a variety of physical quantities including the staggered moments and single-particle spectra at zero temperature to show that the symmetry breaking due to antiferromagnetic ordering occurs in the strong coupling region, whereas in the weak coupling region, the Kondo insulating state without symmetry breaking is realized. The critical interaction strength is estimated. We thus demonstrate that the phase transition due…
Unconventional quantum criticality in heavy-fermion systems has been extensively analyzed in terms of a critical destruction of the Kondo effect. Motivated by a recent demonstration of quantum criticality in a mixed-valent heavy-fermion system, β-YbAlB4, we study a particle-hole-asymmetric Anderson impurity model with a pseudogapped density of states. We demonstrate Kondo destruction at a mixed-valent quantum critical point, where a collapsing Kondo energy scale is accompanied by a singular charge-fluctuation spectrum. Both spin and charge responses scale with energy over temperature (ω/T) and…
We investigate the dynamical charge response of the Anderson model viewed as a quantum RC circuit. Applying a low-energy effective Fermi liquid theory, a generalized Korringa-Shiba formula is derived at zero temperature, and the charge relaxation resistance is expressed solely in terms of static susceptibilities which are accessible by Bethe ansatz. We identify a giant charge relaxation resistance at intermediate magnetic fields related to the destruction of the Kondo singlet. The scaling properties of this peak are computed analytically in the Kondo regime. We also show that the resistance pe…
Non - equilibrium tunneling current of an Anderson impurity system subject to both constant and alternating electric fields is studied. A time - dependent Schrieffer - Wolff transformation maps the time - dependent Anderson Hamiltonian onto a Kondo one. Perturbation expansion in powers of the Kondo coupling strength is carried out up to third order, yielding a remarkably simple analytical expression for the tunneling current. It is found that the zero - bias anomaly is suppressed by an ac - field. Both dc and the first harmonic are equally enhanced by the Kondo effect, while the higher harmoni…
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…
The Friedel oscillations caused due to an impurity located at one edge of a disordered interacting quantum wire are calculated numerically. The electron density in the system's ground state is determined using the DMRG method, and the Friedel oscillations data is extracted using the density difference between the case in which the wire is coupled to an impurity and the case where the impurity is uncoupled. We show that the power law decay of the oscillations occurring for an interacting clean 1D samples described by Luttinger liquid theory, is multiplied by an exponential decay term due to the…
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…
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.
The multi-electron wave function of an interacting electron system depends on the size of the system, i.e. the number of electrons. Here the question investigated is how the wave function changes for a symmetric Friedel-Anderson impurity when the volume is doubled. It turns out that for sufficiently large volume (when the level spacing is smaller than the resonance width) the change in the wave function can be expressed in terms of a universal single-electron state |q> centered at the Fermi level. This electron state is independent of the number of electrons and independent of the parameters o…
Anderson localization (AL) phenomena usually exists in systems with random potential. However, disorder-free quantum many-body systems with local conservation can also exhibit AL or even many-body localization transition. In this work, we show that the AL phase exists in a modified Kondo lattice without external random potential. The density of state, inverse participation ratio and temperature-dependent resistance are computed by classical Monte Carlo simulation, which uncovers the AL phase from previously studied Fermi liquid and Mott insulator regime. The occurrence of AL roots from quenche…
Magnetic properties of uranium and neptunium compounds showing the coexistence of Kondo screening effect and ferromagnetic order are investigated within the Anderson lattice Hamiltonian with a two-fold degenerate $f$-level in each site, corresponding to $5f^2$ electronic configuration with $S=1$ spins. A derivation of the Schrieffer-Wolff transformation is presented and the resulting Hamiltonian has an effective $f$-band term, in addition to the regular exchange Kondo interaction between the $S=1$ $f$-spins and the $s=1/2$ spins of the conduction electrons. The obtained effective Kondo lattice…
