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 numerical results indicate that two ANOs emerge, equal to the number of helical liquids. Specifically, at the coupling symmetry point, both ANOs are fully active with their spatial structures being respectively constituted by the different helical liquids. In comparison, when deviating from the symmetry point, only one ANO remains fully active, which is dominantly constructed by the helical liquid with the larger Kondo coupling. Local screening of the impurity, described by the impurity spin polarization and susceptibility, was further studied. It shows that at the coupling symmetry point, the impurity is maximally polarized and the spin susceptibility reaches the maximum. On the contrary, the impurity tends to be screened without polarization when the Kondo couplings deviate well from the symmetry point. The Kondo screening cloud, manifested by the spin correlation between the impurity and the conduction electrons, was finally explored. It is demonstrated that the Kondo cloud is mainly formed by the helical liquid with the larger Kondo coupling to the impurity. On the other hand, the spin-orbital coupling breaks the symmetry in spatial distribution of the spin correlation, leading to anisotropy in the Kondo cloud.
We use a trial wave function to study the spin-1/2 Kondo effect of a helical metal on the surface of a three-dimensional topological insulator. While the impurity spin is quenched by conduction electrons, the spin-spin correlation of the conduction electron and impurity is strongly anisotropic in both spin and spatial spaces. As a result of strong spin-orbit coupling, the out-of-plane component of the impurity spin is found to be fully screened by the orbital angular momentum of the conduction electrons.
Using the natural orbitals renormalization group (NORG) method, we have investigated the screening of the local spin of an Anderson impurity interacting with the helical edge states in a quantum spin Hall insulator. We find that there is a local spin formed at the impurity site and the local spin is completely screened by electrons in the quantum spin Hall insulator. Meanwhile, the local spin is screened dominantly by a single active natural orbital. We then show that the Kondo screening mechanism becomes transparent and simple in the framework of natural orbitals formalism. We project the act…
We study the conductance of a time-reversal symmetric helical electronic edge coupled antiferromagnetically to a magnetic impurity, employing analytical and numerical approaches. The impurity can reduce the perfect conductance $G_0$ of a noninteracting helical edge by generating a backscattered current. The backscattered steady-state current tends to vanish below the Kondo temperature $T_K$ for time-reversal symmetric setups. We show that the central role in maintaining the perfect conductance is played by a global $U(1)$ symmetry. This symmetry can be broken by an anisotropic exchange couplin…
The combined effect of Rashba and Dresselhaus spin-orbit interactions on the physics of a helical Luttinger liquid coupled to a Kondo impurity is studied. A Rashba coupling can potentially destroy the Kondo singlet formation in certain parameter regimes [Phys. Rev. B 86, 161103(R) (2012)]. This effect is here shown to vanish for sufficiently strong Dresselhaus interaction. The transport properties of the system are investigated by calculating electrical conductance, current and current fluctuations, and thermal conductance.
Transport in an ideal two-dimensional quantum spin Hall device is dominated by the counterpropagating edge states of electrons with opposite spins, giving the universal value of the conductance, $2e^2/h$. We study the effect on the conductance of a magnetic impurity, which can backscatter an electron from one edge state to the other. In the case of isotropic Kondo exchange we find that the correction to the electrical conductance caused by such an impurity vanishes in the dc limit, while the thermal conductance does acquire a finite correction due to the spin-flip backscattering.
The occurrence of two-particle inelastic backscattering has been conjectured in helical edge states of topological insulators and is expected to alter transport. In this Letter, by using a renormalization group approach, we provide a microscopic derivation of this process, in the presence of a time-reversal invariant Rashba impurity potential. Unlike previous approaches to the problem, we are able to prove that such an effect only occurs in the presence of electron-electron interactions. Furthermore, we find that the linear conductance as a function of temperature exhibits a crossover between …
We present a novel technique for the calculation of dynamical correlation functions of quantum impurity systems in equilibrium with Wilson's numerical renormalization group. Our formulation is based on a complete basis set of the Wilson chain. In contrast to all previous methods, it does not suffer from overcounting of excitation. By construction, it always fulfills sum rules for spectral functions. Furthermore, it accurately reproduces local thermodynamic expectation values, such as occupancy and magnetization, obtained directly from the numerical renormalization group calculations.
A complete phase diagram of Zn substituted quantum quasi-two-dimensional helimagnet LiCu2O2 has been presented. Helical ordering transition temperature (T_h) of the original LiCu2O2 follows finite size scaling for less than ~ 5.5% Zn substitution, which implies the existence of finite helimagnetic domains with domain boundaries formed with nearly isolated spins. Higher Zn substitution > 5.5% quenches the long-range helical ordering and introduces an intriguing Zn level dependent magnetic phase transition with slight thermal hysteresis and a universal quadratic field dependence for T_c (Zn > 0.…
We present a new method to calculate directly the one-particle self-energy of an impurity Anderson model with Wilson's numerical Renormalization Group method by writing this quantity as the ratio of two correlation functions. This way of calculating Sigma(z) turns out to be considerably more reliable and accurate than via the impurity Green's function alone. We show results for the self-energy for the case of a constant coupling between impurity and conduction band (ImDelta = const) and the effective Delta(z) arising in the Dynamical Mean Field Theory of the Hubbard model. Implications to the …
We present an alternative functional renormalization group (fRG) approach to the single-impurity Anderson model at finite temperatures. Starting with the exact self-energy and interaction vertex of a small system ('core') containing a correlated site, we switch on the hybridization with a non-interacting bath in the fRG-flow and calculate spectra of the correlated site. Different truncations of the RG-flow-equations and choices of the core are compared and discussed. Furthermore we calculate the linear conductance and the magnetic susceptibility as functions of temperature and interaction stre…
We study the renormalization of a single impurity potential in one-dimensional interacting electron systems in the presence of magnetic field. Using the bosonization technique and Bethe ansatz solutions, we determine the renormalization group flow diagram for the amplitudes of scattering of up- and down-spin electrons by the impurity in a quantum wire at low electron density and in the Hubbard model at less than half filling. In the absence of magnetic field the repulsive interactions are known to enhance backscattering and make the impurity potential impenetrable in the low-energy limit. On t…
We show that the functional renormalization group is a numerically cheap method to obtain the low-energy behavior of the Anderson impurity model describing a localized interacting electron coupled to a bath of conduction electrons. Our approach uses an external magnetic field as flow parameter, partial bosonization of the transverse spin fluctuations, and frequency-independent interaction vertices which are fixed by Ward identities. We calculate the quasi-particle residue and the spin susceptibility in the particle-hole symmetric case and obtain excellent agreement with the Bethe ansatz result…
We present numerical renormalization group (NRG) calculations for a single-impurity Anderson model with a linear coupling to a local phonon mode. We calculate dynamical response functions, spectral densities, dynamic charge and spin susceptibilities. Being non-perturbative, the NRG is applicable for all parameter regimes. Our calculations cover both weak and strong electron-phonon coupling for zero and finite electron-electron interaction. We interpret the high- and low-energy features and compare our results to atomic limit calculations and perturbation theory. In certain restricted parameter…
The impurity Green function and dynamical susceptibilties for the two-channel Anderson impurity model are calculated. An exact expression for the self-energy of the impurity Green function is derived. The imaginary part of the self-energy scales as $\sqrt{|\w/T_K|}$ for $T\to 0$ serving as a hallmark for non-Fermi behavior. The many-body resonance is pinned to a universal value $1/(2πΔ)$ at $\w=0$. Its shape becomes increasingly more symmetric for the Kondo-regimes of the model. The dynamical susceptibilities are governed by two energy scales $T_K$ and $T_h$ and approach a constant value for $…
In this paper we have explored the role of valence fluctuations in an extended Anderson impurity model (e-SIAM) in which there is an additional Hubbard repulsion between conduction and impurity electrons, employing perturbative renormalization methods. We have calculated the scaling equations for the model parameters and solved them both analytically and numerically to find how valence fluctuations renormalize these parameters. Analytical solutions of the scaling equations yielded scaling invariants of the model which we find to be different than the Anderson impurity model signifying differen…
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 introduce a method to obtain the specific heat of quantum impurity models via a direct calculation of the impurity internal energy requiring only the evaluation of local quantities within a single numerical renormalization group (NRG) calculation for the total system. For the Anderson impurity model, we show that the impurity internal energy can be expressed as a sum of purely local static correlation functions and a term that involves also the impurity Green function. The temperature dependence of the latter can be neglected in many cases, thereby allowing the impurity specific heat, $C_{\…
The density matrix renormalization group method is applied to obtain 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. 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 comparis…
We study numerically the universal conductance of Luttinger liquids wire with a single impurity via the Muti-scale Entanglement Renormalization Ansatz (MERA). The scale invariant MERA provides an efficient way to extract scaling operators and scaling dimensions for both the bulk and the boundary conformal field theories. By utilizing the key relationship between the conductance tensor and ground-state correlation function, the universal conductance can be evaluated within the framework of the boundary MERA. We construct the boundary MERA to compute the correlation functions and scaling dimensi…
We calculate the dynamical structure factor S(q, ω) of a weakly interacting helical edge state in the presence of a magnetic field B. The latter opens a gap of width 2B in the single-particle spectrum, which becomes strongly nonlinear near the Dirac point. For chemical potentials |μ| > B, the system then behaves as a nonlinear helical Luttinger liquid, and a mobile-impurity analysis reveals interaction-dependent power-law singularities in S(q,ω). For |μ| < B, the low-energy excitations are gapped, and we determine S(q,ω) by using an analogy to exciton physics.
It has been recently suggested that when an Anderson impurity is immersed in the bulk of a topological insulator, a Kondo resonant peak will appear simultaneously with an in-gap bound-state when the band-dispersion has an "inverted-Mexican-hat" form. The mid-gap bound-state generates another spin state and the Kondo effect is thereby screened. In this paper we study this problem within a weak-coupling RG scheme where we show that the system exhibits complex crossover behavior between different symmetry configurations and may evolve into a self-screened-Kondo or SO(3) low energy fix point. Expe…
We introduce a block Lanczos (BL) recursive technique to construct quasi-one-dimensional models, suitable for density-matrix renormalization group (DMRG) calculations, from single- as well as multiple-impurity Anderson models in any spatial dimensions. This new scheme, named BL-DMRG method, allows us to calculate not only local but also spatially dependent static and dynamical quantities of the ground state for general Anderson impurity models without losing elaborate geometrical information of the lattice. We show that the BL-DMRG method can be easily extended to treat a multi-orbital Anderso…
Using a fermionic renormalization group method we present a simple real space picture of the strong influence an impurity has on the electronic properties of a Luttinger liquid. We compute the flow of the renormalized impurity potential for a single impurity over the entire energy range - from the microscopic scale of a lattice-fermion model down to the low-energy limit. We confirm that low energy properties close to the impurity are as if the chain is cut in two pieces with open boundary conditions at the end points, but show that this universal behavior is only reached for extremely large sy…
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 quasi-1D conducting nanowires spin-orbit coupling destructs spin-charge separation, intrinsic to Tomonaga-Luttinger liquid (TLL). We study renormalization of a single scattering impurity in a such liquid. Performing bosonization of low-energy excitations and exploiting perturbative renormalization analysis we extend the phase portrait in $K_s$ - $K_c$ space, obtained previously for TLL with decoupled spin-charge channels.
We study the Kondo model --a magnetic impurity coupled to a one dimensional wire via exchange coupling-- by using Wilson's numerical renormalization group (NRG) technique. By applying an approach similar to which was used to compute the two impurity problem we managed to improve the bad spatial resolution of the numerical renormalization group method. In this way we have calculated the impurity spin - conduction electron spin correlation function which is a measure of the Kondo compensation cloud whose existence has been a long standing problem in solid state physics. We also present results o…
We study four-terminal junction of spinless Luttinger liquid wires, which describes either a corner junction of two helical edges states of topological insulators or the tunneling from the spinful wire into the helical edge state. We use the fermionic representation and the scattering state formalism, in order to compute the renormalization group (RG) equations for the linear response conductances. We establish our approach by considering a junction between two possibly non-equivalent helical edge states and find an agreement with the earlier analysis of this situation. Tunneling from the tip …
We develop a functional renormalization group approach which describes the low-energy single-particle properties of the Anderson impurity model up to intermediate on-site interactions $U \lesssim 15 Δ$, where $Δ$ is the hybridization in the wide-band limit. Our method is based on a generalization of a method proposed by Schütz, Bartosch and Kopietz [Phys. Rev. B 72, 035107 (2005)], using two independent Hubbard-Stratonovich fields associated with transverse and longitudinal spin fluctuations. Although we do not reproduce the exponentially small Kondo scale in the limit $U \to \infty$, the spin…
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…
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 investigate the effect of spin-orbit coupling on the behavior of magnetic impurity at the edge of a zigzag graphene ribbon by means of quantum Monte Carlo simulations. A peculiar interplay of Kane-Mele type spin-orbit and impurity-host coupling is found to affect local properties such as the impurity magnetic moment and spectral densities. The special helical nature of the topological insulator on the edge is found to affect nonlocal quantities, such as the two-particle and spin-spin correlation functions linking electrons on the impurity with those in the conduction band.
We study the renormalization group flow of the Luttinger-Ward functional and of its two-particle irreducible vertex functions, given a cut-off in the two-particle interaction. We derive a conserving approximation to the flow and relate it to the fluctuation exchange approximation as well as to non-conserving approximations introduced in an earlier publication ctuation exchange approximation as well as to nonconserving approximations introducen [J. F. Rentrop, S. G. Jakobs, and V. Meden, J. Phys. A: Math. Theor. 48, 145002 (2015)]. We apply the different approximate flow equations to the single…
The self-energy method for quantum impurity models expresses the correlation part of the self-energy in terms of the ratio of two Green's functions and allows for a more accurate calculation of equilibrium spectral functions than is possible directly from the one-particle Green's function [Bulla et al., J. Phys.: Condens. Matter 10, 8365 (1998)], for example, within the numerical renormalization group method. In addition, the self-energy itself is a central quantity required in the dynamical mean field theory of strongly correlated lattice models. Here, we show how to generalize the self-energ…
We consider tunneling from the spin-polarized tip into the Luttinger liquid edge state of quantum spin Hall system. This problem arose in context of the spin and charge fractionalization of an injected electron. Renormalization of the dc conductances of the system is calculated in the fermionic approach and scattering states formalism. In lowest order of tunneling amplitude we confirm previous results for the scaling dependence of conductances. Going beyond the lowest order we show that interaction affects not only the total tunneling rate, but also the asymmetry of the injected current. The h…
Quantum impurity problems can be solved using the numerical renormalization group (NRG), which involves discretizing the free conduction electron system and mapping to a `Wilson chain'. It was shown recently that Wilson chains for different electronic species can be interleaved by use of a modified discretization, dramatically increasing the numerical efficiency of the RG scheme [Phys. Rev. B 89, 121105(R) (2014)]. Here we systematically examine the accuracy and efficiency of the `interleaved' NRG (iNRG) method in the context of the single impurity Anderson model, the two-channel Kondo model, …
We study a Kondo impurity model with additional uniaxial anisotropy D in a non-zero magnetic field B using the Numerical Renormalization Group (NRG). The ratio g_e/g_S of electron and impurity g-factor is regarded as a free parameter and, in particular, the special cases of a "local" (g_e=0) and "bulk" (g_e=g_S) field are considered. For a bulk field, the relationship between the impurity magnetization M and the impurity contribution to the magnetization M_imp is investigated. Furthermore, we study how the value of g_e affects the impurity magnetization curves. In case of an isotropic impurity…
We discuss the low-energy physics of the three-orbital Anderson impurity model with the Coulomb interaction term of the Kanamori form which has orbital SO(3) and spin SU(2) symmetry and describes systems with partially occupied $t_{2g}$ shells. We focus on the case with two electrons in the impurity that is relevant to Hund's metals. Using the Schrieffer-Wolff transformation we derive an effective Kondo model with couplings between the bulk and impurity electrons expressed in terms of spin, orbital, and orbital quadrupole operators. The bare spin-spin Kondo interaction is much smaller than the…
An Anderson model for a magnetic impurity in a two-dimensional electron gas with bulk Rashba spin-orbit interaction is solved using the numerical renormalization group under two different experimental scenarios. For a fixed Fermi energy, the Kondo temperature T_K varies weakly with Rashba coupling α, as reported previously. If instead the band filling is low and held constant, increasing αcan drive the system into a helical regime with exponential enhancement of T_K. Under either scenario, thermodynamic properties at low temperatures T exhibit the same dependences on T/T_K as are found for α= …
Using functional methods and the exact renormalization group we derive Ward identities for the Anderson impurity model. In particular, we present a non-perturbative proof of the Yamada-Yosida identities relating certain coefficients in the low-energy expansion of the self-energy to thermodynamic particle number and spin susceptibilities of the impurity. Our proof underlines the relation of the Yamada-Yosida identities to the U(1) x U(1) symmetry associated with particle number and spin conservation in a magnetic field.
We apply a functional implementation of the field-theoretical renormalization group (RG) method up to two loops to the single-impurity Anderson model. To achieve this, we follow a RG strategy similar to that proposed by Vojta \emph{et al.} [Phys. Rev. Lett. \textbf{85}, 4940 (2000)], which consists of defining a soft ultraviolet regulator in the space of Matsubara frequencies for the renormalized Green's function. Then we proceed to derive analytically and solve numerically integro-differential flow equations for the effective couplings and the quasiparticle weight of the present model, which …
We present a technique for calculating non-equilibrium Green functions for impurity systems with local interactions. We use an analogy to the calculation of response functions in the x-ray problem.The initial state and the final state problems, which correspond to the situations before and after the disturbance (an electric or magnetic field, for example) is suddenly switched on, are solved with the aid of Wilson's momentum shell renormalization group. The method is illustrated by calculating the non-equilibrium dynamics of the ohmic two-state problem.
We present the results of a Wilson Renormalization Group study of the single-impurity Kondo and Anderson models in a system with a gap in the conduction electron spectrum. The behavior of the impurity susceptibility and the zero-frequency response function, $T<<S_z; S_z>>$ are discussed in the cases with and without particle-hole symmetry. In addition, for the asymmetric Anderson model the correlation functions, $<\vec S \cdot\vec σ(0)>$,$<n_d>$, and $<n_d(2-n_d)>$ are computed.
Renormalization of non-magnetic impurity potential by strong electron correlation is investigated in detail. We adopt the t-t'-t"-J model and consider mainly a delta-function impurity potential. The variational Monte Carlo method shows that impurity potential scattering matrix elements between Gutzwiller-projected quasi-particle excited states are as strongly renormalized as the hopping terms. Such renormalization is also seen by the Bogoliubov-de Gennes equation with an impurity, where the strong correlation is treated by a Gutzwiller mean-field theory with local Gutzwiller factors and local …
We analyze the ground-state energy, magnetization, magnetic susceptibility, and Kondo screening cloud of the symmetric single-impurity Anderson model (SIAM) that is characterized by the band width $W$, the impurity interaction strength $U$, and the local hybridization $V$. We compare Gutzwiller variational and magnetic Hartree-Fock results in the thermodynamic limit with numerically exact data from the Density-Matrix Renormalization Group (DMRG) method on large rings. To improve the DMRG performance, we use a canonical transformation to map the SIAM onto a chain with half the system size and o…
We develop a general approach to the nonequilibrium dynamics of quantum impurity systems for arbitrary coupling strength. The numerical renormalization group is used to generate a complete basis set necessary for the correct description of the time evolution. We benchmark our method with the exact analytical solution for the resonant-level model. As a first application, we investigate the equilibration of a quantum dot subject to a sudden change of the gate voltage and external magnetic field. Two distinct relaxation times are identified for the spin and charge dynamics.
Following the recent observation of the quantum spin Hall (QSH) effect in HgTe quantum wells, an important issue is to understand the effect of impurities on transport in the QSH regime. Using linear response and renormalization group methods, we calculate the edge conductance of a QSH insulator as a function of temperature in the presence of a magnetic impurity. At high temperatures, Kondo and/or two-particle scattering give rise to a logarithmic temperature dependence. At low temperatures, for weak Coulomb interactions in the edge liquid the conductance is restored to unitarity with unusual …
We analyze the one-dimensional extended Hubbard model with a single static impurity by using a computational technique based on the functional renormalization group. This extends previous work for spinless fermions to spin-1/2 fermions. The underlying approximations are devised for weak interactions and arbitrary impurity strengths, and have been checked by comparing with density-matrix renormalization-group data. We present results for the density of states, the density profile and the linear conductance. Two-particle backscattering leads to striking effects, which are not captured if the bul…
Recent developments in the numerical renormalization group (NRG) allow the construction of the full density matrix (FDM) of quantum impurity models (see A. Weichselbaum and J. von Delft) by using the completeness of the eliminated states introduced by F. B. Anders and A. Schiller (2005). While these developments prove particularly useful in the calculation of transient response and finite temperature Green's functions of quantum impurity models, they may also be used to calculate thermodynamic properties. In this paper, we assess the FDM approach to thermodynamic properties by applying it to t…
Recent experiments with cold atoms on the impurity motion in one-dimensional liquids of interacting bosons have revealed an interesting interplay between the polaronic impurity mass shift and the renormalization of the optical potential. We show that the influence of the external trap on the Bose gas leads to a steeper effective potential for the impurity. We propose a framework in which this potential renormalization and the mass shift can be quantitatively understood by combining a semi-classical theory of density wave excitations in the Luttinger liquid with the non equilibrium formalism of…
A hybrid approach to nonequilibrium dynamics of quantum impurity systems is presented. The numerical renormalization group serves as a means to generate a suitable low-energy Hamiltonian, allowing for an accurate evaluation of the real-time dynamics of the problem up to exponentially long times using primarily the time-adaptive density-matrix renormalization group. We extract the decay time of the interaction-enhanced oscillations in the interacting resonant-level model and show their quadratic divergence with the interaction strength U. Our numerical analysis is in excellent agreement with an…
Many-body correlations in Floquet steady-states: Frequency-resolved renormalization group of the driven Anderson impurity
RWTH Aachen University（亚琛工业大学）；Technische Universität Braunschweig（布伦瑞克工业大学）；Max Planck Institute for the Structure and Dynamics of Matter（马普物质结构动力学研究所）
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…
The numerical renormalization group (NRG) is tailored to describe interacting impurity models in equilibrium, but faces limitations for steady-state nonequilibrium, arising, e.g., due to an applied bias voltage. We show that these limitations can be overcome by describing the thermal leads using a thermofield approach, integrating out high energy modes using NRG, and then treating the nonequilibrium dynamics at low energies using a quench protocol, implemented using the time-dependent density matrix renormalization group (tDMRG). This yields quantitatively reliable results for the current (wit…
We show that to understand the orthogonality catastrophe in the half-filled lattice model of spinless fermions with repulsive nearest neighbor interaction and a local impurity in its Luttinger liquid phase one has to take into account (i) the impurity scaling, (ii) unusual finite size $L$ corrections of the form $\ln(L)/L$, as well as (iii) the renormalization group flow of the umklapp scattering. The latter defines a length scale $L_u$ which becomes exceedingly large the closer the system is to its transition into the charge-density wave phase. Beyond this transition umklapp scattering is rel…
