We identify the precise hallmarks of the local magnetic moment formation and its Kondo screening in the frequency structure of the generalized charge susceptibility. The sharpness of our identification even pinpoints an alternative criterion to determine the Kondo temperature of strongly correlated systems on the two-particle level, which only requires calculations at the lowest Matsubara frequency. We showcase its strength by applying it to the single impurity and the periodic Anderson model as well as to the Hubbard model. Our results represent a significant progress for the general understanding of quantum field theory at the two-particle level and allow for tracing the limits of the physics captured by perturbative approaches in correlated regimes.
Magnetic and charge susceptibilities in the Kondo lattice are derived by the continuous-time quantum Monte Carlo (CT-QMC) method combined with the dynamical mean-field theory. For a weak exchange coupling J and near half filling of the conduction band, antiferromagnetic transition occurs as signalled by divergence of the staggered magnetic susceptibility with lowering temperature. With increasing J, the Kondo effect suppresses the divergence, and the critical value of J agrees well with Doniach's estimate which considers the RKKY interaction as competing with the Kondo effect. For low density …
We propose that the thermoelectric power distinguishes two competing scenarios for quantum phase transitions in heavy fermions : the spin-density-wave (SDW) theory and breakdown of the Kondo effect. In the Kondo breakdown scenario, the Seebeck coefficient turns out to collapse from the temperature scale $E^{*}$, associated with quantum fluctuations of the Fermi surface reconfiguration. This feature differs radically from the physics of the SDW theory, where no reconstruction of the Fermi surface occurs, and can be considered as the hallmark of the Kondo breakdown theory. We test these ideas, u…
The finite-temperature density-matrix renormalization-group method is applied to the one-dimensional Kondo lattice model near half filling to study its thermodynamics. The spin and charge susceptibilities and entropy are calculated down to T=0.03t. We find two crossover temperatures near half filling. The higher crossover temperature continuously connects to the spin gap at half filling, and the susceptibilities are suppressed around this temperature. At low temperatures, the susceptibilities increase again with decreasing temperature when doping is finite. We confirm that they finally approac…
The single impurity Anderson model (SIAM) is studied within an enhanced non-crossing approximation (ENCA). This method is extended to the calculation of susceptibilities and thoroughly tested, also in order to prepare applications as a building block for the calculation of susceptibilities and phase transitions in correlated lattice systems. A wide range of model parameters, such as impurity occupancy, temperature, local Coulomb repulsion and hybridization strength, are studied. Results for the spin and charge susceptibilities are presented. By comparing the static quantities to exact Bethe an…
We present a generic mechanism that explains why many Kondo materials show magnetic ordering along directions that are not favoured by the crystal-field anisotropy. Using a renormalization-group (RG) analysis of single impurity Kondo models with single-ion anisotropy, we demonstrate that strong fluctuations above the Kondo temperature drive a moment re-orientation over a wide range of parameters, e.g. for different spin values $S$ and number of Kondo channels $N$. In tetragonal systems this can happen for both easy-plane or easy axis anisotropy. The characteristic crossing of magnetic suscepti…
Dynamical properties are studied numerically for a variant of the Kondo model with singlet and triplet crystalline electric field (CEF) levels where Kondo and CEF singlets compete for the ground state. Using the continuous-time quantum Monte Carlo method, we derive the $t$-matrix of conduction electrons and dynamical susceptibilities of local electrons without encountering the negative sign problem. When the CEF splitting is comparable to the Kondo temperature, the dynamical response has only a quasi-elastic peak. Nevertheless, the local single-particle spectrum shows an energy gap in strong c…
We analyze the ground-state energy, local spin correlation, impurity spin polarization, impurity-induced magnetization, and corresponding zero-field susceptibilities of the symmetric single-impurity Kondo model on a tight-binding chain with bandwidth $W=2{\cal D}$ and coupling strength $J_{\rm K}$. We compare perturbative results and variational upper bounds from Yosida, Gutzwiller, and first-order Lanczos wave functions to the numerically exact data obtained from the Density-Matrix Renormalization Group (DMRG) and from the Numerical Renormalization Group (NRG) methods. The Gutzwiller variatio…
We consider an interacting nanowire/superconductor heterostructure attached to metallic leads. The device is described by an unusual low-energy model involving spin-1 conduction electrons coupled to a nonlocal spin-1/2 Kondo impurity built from Majorana fermions. The topological origin of the resulting Kondo effect is manifest in distinctive non-Fermi-liquid (NFL) behavior, and the existence of Majorana fermions in the device is demonstrated unambiguously by distinctive conductance lineshapes. We study the physics of the model in detail, using the numerical renormalization group, perturbative …
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…
A model of spin relaxation in Kondo lattices is proposed to explain the presence of an electron spin resonance (ESR) signal in the heavy fermion compounds YbRh2Si2 and YbIr2Si2. Coupled equations for dynamical susceptibilities of Kondo ions and conduction electrons are derived by means of the functional derivative method. The perturbational scaling approach reveals the collective spin motion of Yb ions with conduction electrons in the bottleneck regime. A common energy scale due to the Kondo effect regulates the temperature dependence of the different kinetic coefficients and results in a mutu…
A system of conduction electrons can mediate an indirect magnetic exchange between magnetic impurites. The nonlocal exchange typically competes with the local Kondo screening of the impurity magnetic moments. In case of magnetic adatoms on non-magnetic surfaces this competition is expected to be affected by different confinement effects. Here we study this situation in the regime of intermediate hybridization strengths by means of real-space dynamical mean-field theory for a one-dimensional two-impurity Anderson model. Depending on the presence of a boundary and depending on the system size, a…
We analyse several thermodynamic properties of the two-dimensional Kondo necklace using finite-temperature stochastic series expansion. In agreement with previous zero-temperature findings the model is shown to exhibit a quantum critical point (QCP), separating an antiferromagnetic from a paramagnetic dimerized state at a critical Kondo exchange-coupling strength $J_{c}\approx 1.4$. We evaluate the temperature dependent uniform and staggered structure factors as well as the uniform and staggered susceptibilities and the local 'impurity' susceptibility close to the QCP as well as in the ordered…
We consider a two dimensional Kondo lattice model with exchange J and hopping t in which three out of four impurity spins are removed in a regular way. At the particle-hole symmetric point the model may be studied with auxiliary field quantum Monte Carlo methods without sign problems. To achieve the relevant energy scales on finite clusters, we introduce a simple method to reduce size effects by up to an order of magnitude in temperature. In this model, a metallic phase survives up to arbitrarily low temperatures before being disrupted by magnetic fluctuations which open a gap in the charge se…
Due to the separation between the spin and the orbital screening scales, the normal state of Hund's metals at ambient temperature can be loosely characterized as a partially coherent state with fluctuating spins and quenched orbital moments. With the aim to characterize this situation more precisely, we investigate the Kondo-Kanamori impurity model that describes the low-energy local physics of three-orbital Hund's metals occupied by two or four electrons. Within this model one can diminish the mixed spin-orbital terms and thereby enhance the separation between the two screening scales, allowi…
We consider the local properties of the Yb3+ ion in the crystal electric field in the Kondo lattice compounds YbRh2Si2 and YbIr2Si2. On this basis we have calculated the magnetic susceptibility taking into account the Kondo interaction in the simplest molecular field approximation. The resulting Curie-Weiss law and Van Vleck susceptibilities could be excellently fitted to experimental results in a wide temperature interval where thermodynamic and transport properties show non-Fermi-liquid behaviour for these materials.
We study formation of local magnetic moments in strongly correlated Hubbard model within dynamical mean field theory and associate peculiarities of temperature dependence of local charge $χ_c$ and spin $χ_s$ susceptibilities with different stages of local moment formation. Local maximum of temperature dependence of the charge susceptibility $χ_c$ is associated with beginning of local magnetic moments formation, while the minimum of the susceptibility $χ_c$ and double occupation, as well as low temperature boundary of the plateau of effective local magnetic moment $μ_{\rm eff}^2=Tχ_s$ temperatu…
We grew the single crystal of stoichiometric Tm5Si2.0Ge2.0 using a Bridgeman method and performed XRD, EDS, magnetization, ac and dc magnetic susceptibilities, specific heat, electrical resistivity and XPS experiments. It crystallizes in orthorhombic Sm5Ge4-type structure. The mean valence of Tm ions in Tm5Si2.0Ge2.0 is almost trivalent. The 4f states is split by the crystalline electric field. The ground state exhibits the long range antiferromagnetic order with the ferromagnetically coupled magnetic moments in the ac plane below 8.01 K, while the exited states exhibit the reduction of magnet…
The coherence and phase evolution of electrons in a mesoscopic system in the Kondo correlated regime were studied. The Kondo effect, in turn, is one of the most fundamental many-body effects where a localized spin interacts with conduction electrons in a conductor. Results were obtained by embedding a quantum dot (QD) in a double path electronic interferometer and measuring interference of electron waves. The Phase was found to evolve in a range twice as large as the theoretically predicted one. Moreover, the phase proved to be highly sensitive to the onset of Kondo correlation, thus serving a…
We investigate the quantum transport through Kondo impurity assuming both a large number of orbital channels $\mathcal K$$\gg $$1$ for the itinerant electrons and a semi-classical spin ${\cal S}$ $\gg $ $1$ for the impurity. The non-Fermi liquid regime of the Kondo problem is achieved in the overscreened sector $\mathcal K>2\mathcal{S}$. We show that there exist two distinct semiclassical regimes for the quantum transport through impurity: i) $\mathcal K$ $\gg$ $\mathcal S$ $\gg$ $1$, differential conductance vanishes and ii) $\mathcal S$$/$$\mathcal K{=}\mathcal C$ with $ 0$$<$$\mathcal C$$<$…
Using the numerical renormalization group (NRG) method we study a magnetic impurity coupled to a quantum wire with Rashba and Dresselhaus spin-orbit coupling (SOC) in an external magnetic field. We consider the low-filling regime with the Fermi energy close to the bottom of the band and report the results for local static and dynamic properties in the Kondo regime. In the absence of the field, local impurity properties remain isotropic in spin space despite the SOC-induced magnetic anisotropy of the conduction band. In the presence of the field, clear fingerprints of anisotropy are revealed th…
We investigate the behavior of the dc electronic current, Jdc, in an interacting quantum dot driven by two ac local potentials oscillating with a frequency, Omega0, and a phase-lag, phi. We provide analytical functions to describe the fingerprints of the Coulomb interaction in an experimental Jdc vs phi characteristic curve. We show that the Kondo resonance reduces at low temperatures the frequency range for the linear behavior of Jdc in Omega0 to take place and determines the evolution of the dc-current as the temperature increases.
We study the intersite correlation effects on the Kondo dynamics of two Anderson impurities. Two characteristic energy scales are present associated with the splitting of the uniform and staggered spin susceptibilities. The high energy scale has similar properties as the coherence scale in heavy fermion materials while the low energy scale characterizes the competing orders between Kondo singlet state and inter-impurity singlet state. A singlet superconductivity instability is found near the quantum critical point and is associated with the singular staggered spin susceptibility.
We study the Kondo effect in a CNT(left lead)-CNT(QD)-CNT(right lead) structure. Here CNT is a single-wall metallic carbon nanotube, for which 1) the valence and conduction bands of electrons with zero orbital angular momentum ($m=0$) coalesc at the two valley points ${\bf{K}}$ and ${\bf{K}}'$ of the first Brillouin zone and 2) the energy spectrum of electrons with $m \ne 0$ has a gap whose size is proportional to $|m|$. Following adsorption of hydrogen atoms and application of an appropriately designed gate potential, electron energy levels in the CNT(QD) are tunable to have: 1) two-fold spin…
We consider a magnetic impurity in the antiferromagnetic spin-1/2 chain which is equivalent to the two-channel Kondo problem in terms of the field theoretical description. Using a modification of the transfer-matrix density matrix renormalization group (DMRG) we are able to determine local and global properties in the thermodynamic limit. The cross-over function for the impurity susceptibility is calculated over a large temperature range, which exhibits universal data-collapse. We are also able to determine the local susceptibilities near the impurity, which show an interesting competition of …
We study a Majorana island coupled to a bulk superconductor via a Josephson junction and to multiple external normal leads. In the absence of the Josephson coupling, the system displays a topological Kondo state, which had been largely studied recently. However, we find that this state is unstable even to small Josephson coupling, which instead leads at low temperature $T$ to a new fixed point. Most interesting is the case of three external leads, forming a minimal electronic realization of the long sought two-channel Kondo effect. While the $T=0$ conductance corresponds to simple resonant And…
Scanning tunneling miscoscopy is one of the most powerful spectroscopic tools for single-electron excitations. We show that the conductance fluctuations, or noise in the conductance, of a tunneling current into an interacting electron system is dominated by density-density and spin-spin correlations. This allows one to probe two-particle properties (susceptibilities) and collective excitations by standard experimental tunneling methods. We demonstrate this theoretically, using a novel many-body calculation for the multi-center Kondo problem, including both direct and indirect exchange between …
Quantum Monte Carlo studies of U(1) lattice gauge models of Kondo breakdown
Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg（维尔茨堡大学理论与天体物理研究所及维尔茨堡-德累斯顿ct.qmat卓越集群）
We study a quantum impurity coupled to the edge states of a two-dimensional helical topological superconductor, i.e., to a pair of counterpropagating Majorana fermion edge channels with opposite spin polarizations. For an impurity described by the Anderson impurity model, we show that the problem maps onto a variant of the interacting resonant two-level model which, in turn, maps onto the ferromagnetic Kondo model. Both magnetic and non-magnetic impurities are considered. For magnetic impurities, the bosonization and numerical renormalization group analyses show that the system flows to a fixe…
Magnetic impurity effects on metallic carbon nanotubes are studied theoretically. The resolvent method for the multi channel Kondo effect is applied to the band structure of the kp perturbation hamiltonian in the limit of the infinite onsite repulsion at the impurity site. We discuss the local non-Fermi liquid behavior at temperatures lower than the Kondo temperature T_K. The density of states of localized electron has a singularity |omega|^1/2 which gives rise to a pseudo gap at the Kondo resonance in low temperatures. The temperature dependence of the electronic resistivity is predicted as T…
The Kondo effect typically arises from the spin-flip scattering between the localized magnetic moment of the impurity and the delocalized electrons in the metallic host, which leads to a variety of intriguing phenomena. Here, by using scanning tunnelling microscopy/spectroscopy (STM/STS), we present the Kondo effect and subatomic features of single U adatom on graphene/6H-SiC(0001). A dip spectral feature can be observed around the Fermi energy, which is termed as the "fingerprint" of the Kondo resonance in STS; in addition, two subatomic features with different symmetries: a three-lobe struct…
The two-orbital degenerate Hubbard model with distinct hopping integrals is studied by combining dynamical mean-field theory with quantum Monte Carlo simulations. The role of orbital fluctuations for the nature of the Mott transition is elucidated by examining the temperature dependence of spin, charge and orbital susceptibilities as well as the one-particle spectral function. We also consider the effect of the hybridization between the two orbitals, which is important particularly close to the Mott transition points. The introduction of the hybridization induces orbital fluctuations, resultin…
We study the out of equilibrium steady state properties of the Bose-Fermi-Kondo model, describing a local magnetic moment coupled to two ferromagnetic leads that support bosonic (magnons) and fermionic (Stoner continuum electrons) low energy excitations. This model describes the destruction of the Kondo effect as the coupling to the bosons is increased. Its phase diagram comprises three non-trivial fixed points. Using a dynamical large-$N$approach on the Keldysh contour, we study two different non-equilibrium setups: (a) a finite bias voltage and (b) a finite temperature gradient, imposed acro…
The numerical renormalization group is employed to study a double quantum (DQD) dot system consisting of two equivalent single-level dots, each coupled to its own lead and with a mutual capacitive coupling embodied in an interdot interaction U', in addition to the intradot Coulomb interaction U. We focus on the regime with two electrons on the DQD, and the evolution of the system on increasing U'/U. The spin-Kondo effect arising for U'=0 (SU(2) x SU(2)) is found to persist robustly with increasing U'/U, before a rapid but continuous crossover to (a) the SU(4) point U'=U where charge and spin d…
We present a quantum embedding methodology to resolve the Anderson impurity model in the context of dynamical mean-field theory, based on an extended exact diagonalization method. Our method provides a maximally localized quantum impurity model, where the non-local components of the correlation potential remain minimal. This method comes at a large benefit, as the environment used in the quantum embedding approach is described by propagating correlated electrons and hence offers a polynomial increase $O(N^4)$ of the number of degrees of freedom for the embedding mapping without adding bath sit…
We study the effect of the formation and screening of local magnetic moments on the temperature- and interaction dependencies of spectral functions and resistivity in the vicinity of the metal-insulator transition. We use the dynamical mean-field theory for the strongly correlated Hubbard model and associate the peculiarities of the above mentioned properties with those found for the local charge $χ_c$ and spin $χ_s$ susceptibilities. We show that at half filling the maximum of resistivity at a certain temperature $T^*$ corresponds to the appearance of central quasiparticle peak of the spectra…
We study the response of classical impurities in quantum Ising chains. The Z2 degeneracy they entail renders the existence of two decoupled Majorana modes at zero energy an exact property of a finite system at arbitrary values of its bulk parameters. We trace the evolution of these modes across the transition from the disordered phase to the ordered one and analyze the concomitant qualitative changes of local magnetic properties of an isolated impurity. In the disordered phase, the two ground states differ only close to the impurity, and they are related by the action of an explicitly construc…
