Anderson Impurity Model Research Articles

Foundations of variational discrete action theory

A new variational theory is proposed, based on the sequential product density matrix (SPD) ansatz, which is characterized by an integer and monotonically approaches the exact solution. The authors introduce the discrete action theory to evaluate the SPD, yielding the variational discrete action theory (VDAT). VDAT can be exactly evaluated for the multiband Anderson impurity model and the multiband Hubbard model in infinite dimensions. This provides an unprecedented combination of efficiency and precision within a single framework.

Many-body wavefunctions for quantum impurities out of equilibrium. II. Charge fluctuations

We extend the general formalism discussed in the previous paper [A. B. Culver and N. Andrei, Phys. Rev. B 103, 195106 (2021)] to two models with charge fluctuations: the interacting resonant level model and the Anderson impurity model. In the interacting resonant level model, we find the exact time-evolving wavefunction and calculate the steady state impurity occupancy to leading order in the interaction. In the Anderson impurity model, we find the nonequilibrium steady state for small or large Coulomb repulsion $U$, and we find that the steady state current to leading order in $U$ agrees with a Keldysh perturbation theory calculation.

Many-body wavefunctions for quantum impurities out of equilibrium

We present a method for calculating the time-dependent many-body wavefunction that follows a local quench. We apply the method to the voltage-driven nonequilibrium Kondo model to find the exact time-evolving wavefunction following a quench where the dot is suddenly attached to the leads at $t=0$. The method, which does not use Bethe ansatz, also works in other quantum impurity models (we include results for the interacting resonant level and the Anderson impurity model) and may be of wider applicability. In the particular case of the Kondo model, we show that the long-time limit (with the system size taken to infinity first) of the time-evolving wavefunction is a current-carrying nonequilibrium steady state that satisfies the Lippmann-Schwinger equation. We show that the electric current in the time-evolving wavefunction is given by a series expression that can be expanded either in weak coupling or in strong coupling, converging to all orders in the steady-state limit in either case. The series agrees to leading order with known results in the well-studied regime of weak antiferromagnetic coupling and also reveals another universal regime of strong ferromagnetic coupling, with Kondo temperature $T_K^{(F)} = D e^{-\frac{3\pi^2}{8} \rho |J|}$ ($J<0$, $\rho|J|\to\infty$). In this regime, the differential conductance $dI/dV$ reaches the unitarity limit $2e^2/h$ asymptotically at large voltage or temperature.

Asymptotics of the eigenvalues of the Anderson Hamiltonian with white noise potential in two dimensions

In this paper we consider the Anderson Hamiltonian with white noise potential on the box [0,L]2 with Dirichlet boundary conditions. We show that all of the eigenvalues divided by logL, converge as L→∞, almost surely to the same deterministic constant which is given by a variational formula.

Footprints of impurity quantum phase transitions in quantum Monte Carlo statistics

Interacting single-level quantum dot connected to BCS superconducting leads represents a well-controllable system to study the interplay between the correlation effects and the electron pairing that can result in a $0-\pi$ (singlet-doublet) quantum phase transition. The physics of this system can be well described by the impurity Anderson model. We present an analysis of the statistics of the perturbation expansion order of the continuous-time hybridization expansion quantum Monte Carlo algorithm in the vicinity of such a first-order impurity quantum phase transition. By calculating the moments of the histograms of the expansion order which deviate from the ideal Gaussian shape, we provide an insight into the thermodynamic mixing of the two phases at low but finite temperatures which is reflected in the bimodal nature of the histograms.

Quantum quasi Monte Carlo algorithm for out-of-equilibrium Green functions at long times

We extend the recently developed quantum quasi Monte Carlo (QQMC) approach to obtain the full frequency dependence of Green functions in a single calculation. QQMC is a general approach for calculating high-order perturbative expansions in power of the electron-electron interaction strength. In contrast to conventional Markov chain Monte Carlo sampling, QQMC uses low-discrepancy sequences for a more uniform sampling of the multidimensional integrals involved and can potentially outperform Monte Carlo by several orders of magnitude. A core concept of QQMC is the a priori construction of a ``model function'' that approximates the integrand and is used to optimize the sampling distribution. In this paper, we show that the model function concept extends to a kernel approach for the computation of Green functions. We illustrate the approach on the Anderson impurity model and show that the scaling of the error with the number of integrand evaluations $N$ is $\ensuremath{\sim}1/{N}^{0.86}$ in the best cases and comparable to Monte Carlo scaling $\ensuremath{\sim}1/{N}^{0.5}$ in the worst cases. We find a systematic improvement over Monte Carlo sampling by at least two orders of magnitude while using a basic form of model function. Finally, we compare QQMC results with calculations performed with the fork tensor product state (FTPS) method, a recently developed tensor network approach for solving impurity problems. Applying a simple Pad\'e approximant for the series resummation, we find that QQMC matches the FTPS results beyond the perturbative regime.

Revealing strong correlations in higher-order transport statistics: A noncrossing approximation approach

We present a method for calculating the full counting statistics of a nonequilibrium quantum system based on the propagator noncrossing approximation (NCA). This numerically inexpensive method can provide higher order cumulants for extended parameter regimes, rendering it attractive for a wide variety of purposes. We compare NCA results to Born-Markov quantum master equations (QME) results to show that they can access different physics, and to numerically exact inchworm quantum Monte-Carlo data to assess their validity. As a demonstration of its power, the NCA method is employed to study the impact of correlations on higher order cumulants in the nonequilibrium Anderson impurity model. The four lowest order cumulants are examined, allowing us to establish that correlation effects have a profound influence on the underlying transport distributions. Higher order cumulants are therefore demonstrated to be a proxy for the presence of Kondo correlations in a way that cannot be captured by simple QME methods.

Electronic structure and magnetic properties of Dy-doped Bi2Te3

The electronic and magnetic character, and the magnetic anisotropy in practically important magnetic materials containing the rare earth elements are investigated making use of the correlated band theory implemented as a combination of the relativistic density functional theory with the Anderson impurity model (DFT+U+HIA). First, we demonstrate that DFT+U+HIA provides a good description of the electronic structure, spin and orbital magnetic moments, and the magnetic anisotropy for SmCo5 magnet with 4f5-like Sm3+ shell. Further, the method is applied to theoretical investigation of Dy-doped Bi2Te3 topological insulator. For both ferro- and anti-ferromagnetic Dy-planes in Bi2Te3 we found the in-gap flat f-bands located at the top of the valence band of Bi2Te3. The positive uniaxial MAE is predicted for (DyxBi1−x)2Te3 with x = 0.33. The experimental resonant photoemission spectra are well reproduced by the calculations. These studies can be important to explore the potential use of rare-earth doped topological insulators in the low-power spintronic devises.

Resistivity minimum emerges in Anderson impurity model modified with Sachdev–Ye–Kitaev interaction* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11674139, 11704166, and 11834005) and the Fundamental Research Funds for the Central Universities, China, and PCSIRT (Grant No. IRT-16R35).

We investigate a modified Anderson model at the large-N limit, where the Coulomb interaction is replaced by the Sachdev–Ye–Kitaev random interaction. The resistivity of conduction electron ρ c has a minimum value around temperature T*, which is similar to the Kondo system, but the impurity electron’s density of state A d(ω) demonstrates no sharp-peak like the Kondo resonance around the Fermi surface. This provides a counterintuitive example where resistivity minimum exists without Kondo resonance. The impurity electron’s entropy S d and specific heat capacity C v show a crossover from Fermi liquid to a non-Fermi liquid behavior dependent on temperature. The system is a Fermi liquid at T < T*, and becomes a non-Fermi liquid at T > T*, and then becomes a Fermi gas at sufficiently high temperatures T ≫ T*. The non-Fermi liquid at the intermediate-T regime does not occur in the standard Anderson model. We also make a renormalization group analysis, which confirms the crossover from Fermi liquid to the non-Fermi behavior. It is emphasized that the resistivity minimum emerges in our model when the system behaves as a non-Fermi liquid rather than Fermi liquid, which provides an alternative example showing resistivity minimum in condensed matter physics.

Magnetic and electronic properties of transition metal doped aluminium nitride: Haldane’s approach combined with ab initio results

The electronic and magnetic properties of transition metal (Mn and Cr) doped Aluminium Nitride (AlN) in the wurtzite structure is studied using the single impurity Anderson model (SIAM) extended to semiconductors by Haldane. An equation of motion method based on Green’s function was used to obtain the effective spin decomposed impurity levels. The calculated electronic density of states of Mn and Cr valence orbitals exhibit half metallic properties when the impurity is strongly coupled to the host. The effect of the Coulomb correlation and orbital hybridization on the formation of a localized moment in such systems is investigated. Magnetic impurities are often responsible for the inelastic scattering of conduction electrons. For a configuration averaged random ensemble of impurities, initially non-polarized host band develops a small moment presumably due to the potential scattering.

Dicke and Fano-Andreev reflections in a triple quantum-dot system

This article studies quantum interference effects and their influence on the electronic transport through a parallel triple quantum-dot system coupled to normal and superconducting leads in the linear response and non-equilibrium regime. We model the system by a triple impurity Anderson Hamiltonian including the Coulomb intra-dot correlations in all quantum-dots. Using the non-equilibrium Green’s function formalism, we calculate the Andreev conductance and the transmittance for energies within the superconductor gap. Our results show that the Andreev reflection spectra, both in the presence and absence of Coulomb interaction, reveal Fano and Dicke-like resonances in analogy to the Fano and Dicke effects in atomic physics. As one of the main results, we obtain that the charge shows abrupt changes due to the Dicke effect.

Kondo screening regimes in multi-Dirac and Weyl systems

We have investigated the Kondo physics of a single magnetic impurity embedded in multi-Dirac (Weyl) node fermionic systems. By using a generic effective model for the host material and employing a numerical renormalization group approach we access the low temperature behavior of the system, identifying the existence of Kondo screening in single-, double-, and triple-Dirac (Weyl) node models. We find that in any multi-Dirac node systems the low-energy regime lies within one of the known classes of pseudogap Kondo problem, extensively studied in the literature. Kondo screening is also observed for time reversal symmetry broken Weyl systems. This is, however, possible only in the particle-hole symmetry broken regime obtained for finite chemical potential $\mu$. Although weakly, breaking time-reversal symmetry suppresses the Kondo resonance, especially in the single-node Weyl semimetals. More interesting Kondo screening regimes are obtained for inversion symmetry broken multi-Weyl fermions. In these systems the Kondo regimes of double- and triple-Weyl node models are much richer than in the single-Weyl node model. While in the single-Weyl node model the Kondo temperature increases monotonically with $|\mu|$ regardless the value of the inversion symmetry breaking parameter $Q_0$, in double- and triple-Weyl node models there are two distinct regimes: (i) For $Q_0< |\mu|$ the Kondo temperature depends strongly on $\mu$, while (ii) for $Q_0 > |\mu|$ the Kondo temperature depends very weakly on $\mu$, resembling the flat-band single impurity Anderson model.

Spectral and transport properties of a half-filled Anderson impurity coupled to phase-biased superconducting and metallic leads

We derive and apply a general scheme for mapping a setup consisting of a half-filled single-level quantum dot coupled to one normal metallic and two superconducting phase-biased leads onto an ordinary half-filled single impurity Anderson model with single modified tunneling density of states. The theory allows for the otherwise unfeasible application of the standard numerical renormalization group and enables us to obtain phase-dependent local spectral properties as well as phase-dependent induced pairing and Josephson current. The resulting transport properties match well with the numerically exact continuous-time hybridization-expansion quantum Monte Carlo. For weakly coupled normal electrode, the spectral properties can be interpreted in terms of normal-electrode-broadened Andreev bound states with phase-dependent position analogous to the superconducting Anderson model, which coexist in the $\ensuremath{\pi}$-like phase with a Kondo peak whose phase-dependent Kondo temperature is extracted.

Time dependent reduced density matrix functional theory at strong correlation: insights from a two-site Anderson impurity model.

The one-body density matrix has recently attracted considerable attention as a promising key quantity for the description of systems out of equilibrium. Its time evolution is given in terms of the two-body density matrix, and thus the central challenge is to find approximations to the latter. An extra layer of difficulty is added when dealing with strong electron correlations. In this work, we explore precisely this regime by looking at the two-site Anderson impurity model as a case study. To address the system's dynamics, we use an adiabatic approximation based on the exact ground-state two-body density matrix. We find that this adiabatic extension does not reproduce the exact results even for a slow switch-on of the external perturbation, and we trace back this behavior to the lack of an accurate imaginary part of the adiabatic approximation to the two-body density matrix. The attempt to restore an approximate imaginary part through a Hilbert transform of the real part works well only for very short times, but quickly deteriorates for longer times, with the one-body density matrix being pushed out of its N-representability domain. Our results thus pose an important constraint on practical prescriptions to perform the time evolution of the one-body density matrix.

Influence of superconductivity on the magnetic moment of quantum impurity embedded in BCS superconductor

We study the influence of superconductivity on the formation of the localized magnetic moment for a single-level quantum impurity embedded in an s-wave Bardeen–Cooper–Schrieffer (BCS) superconducting medium, modeled by single-impurity Anderson Hamiltonian. We have combined Bogoliubov transformation with Green’s function method within self-consistent Hartree–Fock mean field approximation to analyze the conditions necessary in metal (in the superconducting) for the formation of the magnetic moment at the impurity site for the low-frequency limit |ω| ≪ Δsc as well as for the finite superconducting gap Δsc. We have compared these results with other theoretical results and with the single-level quantum impurity embedded in the normal metallic host. Further, we analyze the spectral density of the quantum impurity embedded in a superconducting host to study the sub-gap states as a function of impurity parameters.

Quasiparticle Mass Enhancement as a Measure of Entanglement in the Kondo Problem.

We analyze the quantum entanglement between opposite spin projection electrons in the ground state of the Anderson impurity model. In this model, a single level impurity with intralevel repulsion U is tunnel coupled to a free electron gas. The Anderson model presents a strongly correlated many body ground state with mass enhanced quasiparticle excitations. We find, using both analytical and numerical tools, that the quantum entanglement between opposite spin projection electrons is a monotonic universal function of the quasiparticle mass enhancement Z in the Kondo regime. This indicates that the interaction induced mass enhancement, which is generally used to quantify correlations in quantum many body systems, could be used as a measure of entanglement in the Kondo problem.

Quantum Critical Point between Two-Channel Kondo and Fermi-Liquid Phases

We investigate the emergence of quantum critical points near a two-channel Kondo phase by evaluating an $f$-electron entropy of a seven-orbital impurity Anderson model hybridized with three ($\Gamma_7$ and $\Gamma_8$) conduction bands with the use of a numerical renormalization group method First we consider the case of Pr$^{3+}$ ion, in which quadrupole two-channel Kondo effect is known to occur for the local $\Gamma_3$ doublet state. When we control crystalline electric field (CEF) potentials so as to change the local CEF ground state from $\Gamma_3$ doublet to $\Gamma_1$ singlet or $\Gamma_5$ triplet, we commonly observe a residual entropy of $\log \phi$ with the golden ratio $\phi=(1+\sqrt{5})/2$, which is equal to that for three-channel Kondo effect. This peculiar residual entropy is also observed for the case of Nd$^{3+}$ ion, in which magnetic two-channel Kondo phase is found to occur for the local $\Gamma_6$ doublet state. We envisage a scenario that the quantum critical point characterized by $\log \phi$ generally appears between two-channel Kondo and Fermi-liquid phases.

Quantum phase transitions and the role of impurity-substrate hybridization in Yu-Shiba-Rusinov states

Spin-dependent scattering from magnetic impurities inside a superconductor gives rise to Yu-Shiba-Rusinov (YSR) states within the superconducting gap. They can be modeled by the largely equivalent Kondo or Anderson impurity models. The role of the magnetic and nonmagnetic properties of the impurity in relation to the coupling to the substrate is still under debate. Here, we use a scanning tunneling microscope to make a quantitative connection between the energy of a YSR state and the impurity-substrate hybridization. We corroborate the impurity substrate coupling as a key energy scale for surface derived YSR states using the Anderson impurity model. By combining experimental data from YSR state spectra and additional conductance measurements, we can determine on which side of the quantum phase transition the system resides. We thus provide a crucial step towards a more quantitative understanding of the crucial role of impurity substrate coupling utilizing the Anderson model.

Impurity resonance effects in graphene versus impurity location, concentration, and sublattice occupation

Unique electronic band structure of graphene with its semi-metallic features near the charge neutrality point is sensitive to impurity effects. Using the Lifshitz and Anderson impurity models, we study in detail the disorder induced spectral phenomena in the electronic band structure of graphene, namely, the formation of resonances, quasi-gaps, bound states, impurity sub-bands, and their overall impact on the electronic band restructuring and the associated Mott-like metal-insulator transitions. We perform systematic analytical and numerical study for realistic impurities, both substitutional and adsorbed, focusing on those effects that stem from the impurity adatoms locations (top, bridge, and hollow positions), concentration, host sublattice occupation, perturbation strengths, etc. Possible experimental and practical implications are discussed as well.

A molecular shift register made using tunable charge patterns in one-dimensional molecular arrays on graphene

The ability to tune the electronic properties of molecular arrays is an important step in the development of molecule-scale electronic devices. However, control over internal device charge distributions by tuning interactions between molecules has proved challenging. Here, we show that gate-tunable charge patterning can occur in one-dimensional molecular arrays on graphene field-effect transistors. One-dimensional molecular arrays are fabricated using an edge-templated self-assembly process that allows organic molecules (F4TCNQ) to be precisely positioned on graphene devices. The charge configurations of the molecular arrays can be reversibly switched between different collective charge states by tuning the graphene Fermi level via a back-gate electrode. Charge pinning at the ends of the molecular arrays allows the charge state of the entire array to be controlled by adding or removing an edge molecule and changing the total number of molecules in an array between odd and even integers. Charge patterns altered in this way propagate down the array in a cascade effect, allowing the array to function as a charge-based molecular shift register. An extended multi-site Anderson impurity model is used to quantitatively explain this behaviour. One-dimensional molecular arrays on graphene field-effect transistors can be reversibly switched between different periodic charge states by tuning the graphene Fermi level via a back-gate electrode and by manipulating individual molecules, allowing them to function as a nanoscale shift register.