Single-impurity Anderson Model Research Articles

Real-frequency quantum field theory applied to the single-impurity Anderson model

Real-frequency quantum field theory applied to the single-impurity Anderson model

Impact of the states in the electronic structure of the intermediate-valence superconductor CeIr3

The electronic structure of the f-based superconductor was studied by photoelectron spectroscopy. The energy distribution of the states were revealed by the resonant photoelectron spectroscopy. The states were mostly distributed in the vicinity of the Fermi energy, suggesting the itinerant character of the states. The contribution of the states to the density of states (DOS) at the Fermi energy was estimated to be nearly half of that of the states, implying that the states have a considerable contribution to the DOS at the Fermi energy. The core-level and x-ray absorption spectra were analyzed based on a single-impurity Anderson model. The number of the states in the ground state was estimated to be , which is much larger than the values obtained in the previous studies (i.e. ).

An efficient Julia framework for hierarchical equations of motion in open quantum systems

The hierarchical equations of motion (HEOM) approach can describe the reduced dynamics of a system simultaneously coupled to multiple bosonic and fermionic environments. The complexity of exactly describing the system-environment interaction with the HEOM method usually results in time-consuming calculations and a large memory cost. Here, we introduce an open-source software package called HierarchicalEOM.jl: a Julia framework integrating the HEOM approach. HierarchicalEOM.jl features a collection of methods to compute bosonic and fermionic spectra, stationary states, and the full dynamics in the extended space of all auxiliary density operators (ADOs). The required handling of the ADOs multi-indexes is achieved through a user-friendly interface. We exemplify the functionalities of the package by analyzing a single impurity Anderson model, and an ultra-strongly coupled charge-cavity system interacting with bosonic and fermionic reservoirs. HierarchicalEOM.jl achieves a significant speedup with respect to the corresponding method in the Quantum Toolbox in Python (QuTiP), upon which this package is founded.

Universal scaling of tunable Yu-Shiba-Rusinov states across the quantum phase transition

Quantum magnetic impurities give rise to a wealth of phenomena attracting tremendous research interest in recent years. On a normal metal, magnetic impurities generate the correlation-driven Kondo effect. On a superconductor, bound states emerge inside the superconducting gap called the Yu-Shiba-Rusinov (YSR) states. Theoretically, quantum impurity problems have been successfully tackled by numerical renormalization group (NRG) theory, where the Kondo and YSR physics are shown to be unified and the normalized YSR energy scales universally with the Kondo temperature divided by the superconducting gap. However, experimentally the Kondo temperature is usually extracted from phenomenological approaches, which gives rise to significant uncertainties and cannot account for magnetic fields properly. Using scanning tunneling microscopy at 10 mK, we apply a magnetic field to several YSR impurities on a vanadium tip to reveal the Kondo effect and employ the microscopic single impurity Anderson model with NRG to fit the Kondo spectra in magnetic fields accurately and extract the corresponding Kondo temperature unambiguously. Some YSR states move across the quantum phase transition (QPT) due to the changes in atomic forces during tip approach, yielding a continuous universal scaling with quantitative precision for quantum spin-frac{1}{2} impurities.

A multi-fragment real-time extension of projected density matrix embedding theory: Non-equilibrium electron dynamics in extended systems.

In this work, we derive a multi-fragment real-time extension of the projected density matrix embedding theory (pDMET) designed to treat non-equilibrium electron dynamics in strongly correlated systems. As in the previously developed static pDMET, the real time pDMET partitions the total system into many fragments; the coupling between each fragment and the rest of the system is treated through a compact representation of the environment in terms of a quantum bath. The real-time pDMET involves simultaneously propagating the wavefunctions for each separate fragment-bath embedding system along with an auxiliary mean-field wavefunction of the total system. The equations of motion are derived by (i) projecting the time-dependent Schrödinger equation in the fragment and bath space associated with each separate fragment and by (ii) enforcing the pDMET matching conditions between the global 1-particle reduced density matrix (1-RDM) obtained from the fragment calculations and the mean-field 1-RDM at all points in time. The accuracy of the method is benchmarked through comparisons to time-dependent density-matrix renormalization group and time-dependent Hartree-Fock (TDHF) theory; the methods were applied to a one- and two-dimensional single-impurity Anderson model and multi-impurity Anderson models with ordered and disordered distributions of the impurities. The results demonstrate a large improvement over TDHF and rapid convergence to the exact dynamics with an increase in fragment size. Our results demonstrate that the real-time pDMET is a promising and flexible method that balances accuracy and efficiency to simulate the non-equilibrium electron dynamics in heterogeneous systems of large size.

Quantum transport via dot devices with arbitrarily strong interactions

The paper develops a theory of tunneling electron transport through atomic-scale systems (or briefly quantum dots) with arbitrarily strong interaction. The theory is based on a diagram technique for nonequilibrium Green’s functions defined on Hubbard operators. The use of Hubbard operators, describing many-body states of an entire quantum dot, makes it possible to represent the Hamiltonian of the quantum dot in a universal diagonal form and consider its coupling with two leads within the perturbation theory. It is shown that in the case when all Hubbard operators are defined for the same site, some rules of the diagram technique for Hubbard operators, initially developed for lattice models, have to be modified. As an example of the application of the modified theory, the current-voltage characteristics of the single-impurity Anderson model with infinitely large Coulomb repulsion are calculated. It is shown that taking into account the multiple electron tunneling processes with spin flips results in the dip in the center of the Lorentz distribution peak, describing the density of states of the one level Anderson impurity coupled with two leads. The emergence of this dip in the density of states leads to a peculiar feature in the bias voltage dependence of the differential conductivity, which can be detected experimentally.

Mapping renormalized coupled cluster methods to quantum computers through a compact unitary representation of nonunitary operators

Nonunitary theories are commonly seen in the classical simulations of quantum systems. Among these theories, the method of moments of coupled cluster equations (MMCCs) and the ensuing classes of the renormalized coupled cluster (CC) approaches have evolved into one of the most accurate approaches to describe correlation effects in various quantum systems. The MMCC formalism provides an effective way for correcting the energies of approximate CC formulations (parent theories) using moments, or CC equations, that are not used to determine approximate cluster amplitudes. In this paper, we propose a quantum algorithm for computing MMCC ground-state energies that provides two main advantages over classical computing or other quantum algorithms: (i) the possibility of forming superpositions of CC moments of arbitrary ranks in the entire Hilbert space and using an arbitrary form of the parent cluster operator for MMCC expansion, and (ii) significant reduction in the number of measurements in quantum simulation through a compact unitary representation for a generally nonunitary operator. We illustrate the robustness of our approach over a broad class of test cases, including $\ensuremath{\sim}40$ molecular systems with varying basis sets encoded using 4--40 qubits, and we exhibit the detailed MMCC analysis for the 8-qubit half-filled, four-site, single impurity Anderson model and the 12-qubit hydrogen fluoride molecular system from the corresponding noise-free and noisy MMCC quantum computations. We also outline the extension of the MMCC formalism to the case of a unitary CC wave-function Ansatz.

Level occupation switching with density functional theory

The charge transport properties of zero-temperature multiorbital quantum dot systems with one dot coupled to leads and the other dots coupled only capacitatively are studied within density functional theory. It is shown that the setup is equivalent to an effective single impurity Anderson model. This allows to understand the level occupation switching effect as transitions between ground states of different integer occupations in the uncoupled dots. Level occupation switching is very sensitive to small energy differences and therefore also to the details of the parametrized exchange-correlation functionals. An existing functional already captures the effect on a qualitative level, but we also provide an improved parametrization which is very accurate when compared to reference numerical renormalization group results.

Spatial spin-spin correlations of the single-impurity Anderson model with a ferromagnetic bath

We investigate the interplay between the Kondo effect and the ferromagnetism by an one dimension Anderson impurity model with a spin partially polarized bath, using the projective truncation approximation under Lacroix basis.The equal-time spatial spin-spin correlation function (SSCF) is calculated. For the case of spin-unpolarized conduction electrons, it agrees qualitatively with the results from density matrix renormalization group (DMRG). For system with partially spin-polarized conduction electrons, an oscillation in the envelope of SSCF emerges due to the beating of two Friedel oscillations associated to two spin-split Fermi surfaces of conduction electrons. The period is proportional to the inverse of magnetic field $h$. A fitting formula is proposed to perfectly fits the numerical results of SSCF in both the short- and long-range regions. For large enough bath spin polarization, a bump appears in the curve of the integrated SSCF. It marks the boundary between the suppressed Kondo cloud and the polarized bath sites.

Neural Network Solver for Small Quantum Clusters

Machine learning approaches have recently been applied to the study of various problems in physics. Most of these studies are focused on interpreting the data generated by conventional numerical methods or the data on an existing experimental database. An interesting question is whether it is possible to use a machine learning approach, in particular a neural network, for solving the many-body problem. In this paper, we present a neural network solver for the single impurity Anderson model, the paradigm of an interacting quantum problem in small clusters. We demonstrate that the neural-network-based solver provides quantitative accurate results for the spectral function as compared to the exact diagonalization method. This opens the possibility of utilizing the neural network approach as an impurity solver for other many-body numerical approaches, such as the dynamical mean field theory.

Enhanced Spin Transfer Torque in Single Barrier Model Tunnel Junctions Containing Disordered Interface

We investigate the role of magnetic impurities in the barrier region in enhancing the torque transferred to the free ferromagnet layer in a non-collinear model tunnel junction. The tunnel junction is modeled using the non-equilibrium Green’s function formalism within the tight-binding approximation. The position of the impurity which is described by the single impurity Anderson model is found to have a profound impact on the trends observed in the spin transfer torque. The parallel ([Formula: see text]) torque is observed to have a switch on-off step-like bias behavior while the perpendicular ([Formula: see text]) torque exhibits a change in sign between the switch-on bias voltages. The spin transfer torque is found to be dramatically enhanced when the impurity is positioned at the interface of a five-layer barrier which is three orders of magnitude larger even at temperatures as high as 200[Formula: see text]K. With this formulation the effect of Coulomb repulsion at the impurity site on the torque could be deduced and the obtained results are explained in terms of the region-wise electronic density of states in the junction.

Algebraic equation of motion approach for solving the Anderson model

Based on the algebraic equation of motion (AEOM) approach, we have studied the single-impurity Anderson model by analytically solving the AEOM of the f-electron one-particle Green function in the Kondo limit. The related spectral function satisfies the sum rule and shows that there is a well-known three-peak structure at zero temperature. In the low energy limit, we obtain the analytical formula of the Kondo temperature that is the same as the exact solution in form except for a prefactor. We also show that the shape of the Kondo resonance is the Lorentzian form and the corresponding weight is proportional to the spin-flip correlation function.

Resonant inelastic x-ray scattering of spin-charge excitations in a Kondo system

Resonant inelastic x-ray scattering (RIXS) studies across the Ce ${M}_{5}$ edge have been carried out to investigate the electronic structure of the ferromagnetic ${\mathrm{CeAgSb}}_{2}$ Kondo system. The RIXS spectra exhibit energy loss features corresponding to final states usually observed by combining photoemission and inverse photoemission spectroscopy. At low energy loss, a clear signature of the spectral features corresponding to the spin-orbit interaction is also observed. Polarization dependence provides evidence for the ${}^{1}{S}_{0}$ symmetry singlet ground state by a total suppression of the ${f}^{0}$ final state. A simplified single-impurity Anderson model combined with full multiplet theory allows an accurate description of the spin-charge excitations. The RIXS data also reveal a strong temperature $T$ dependence of the fluorescencelike structure. We conjecture that this behavior reflects the $T$ dependence of the Kondo resonance.

Singlet-Doublet Transitions of a Quantum Dot Josephson Junction Detected in a Transmon Circuit

We realize a hybrid superconductor-semiconductor transmon device in which the Josephson effect is controlled by a gate-defined quantum dot in an InAs-Al nanowire. Microwave spectroscopy of the transition spectrum of the transmon allows us to probe the ground-state parity of the quantum dot as a function of the gate voltages, the external magnetic flux, and the magnetic field applied parallel to the nanowire. The measured parity phase diagram is in agreement with that predicted by a single-impurity Anderson model with superconducting leads. Through continuous-time monitoring of the circuit, we furthermore resolve the quasiparticle dynamics of the quantum dot Josephson junction across the phase boundaries. Our results can facilitate the realization of semiconductor-based 0-π qubits and Andreev qubits.Received 28 February 2022Revised 23 May 2022Accepted 24 May 2022DOI:https://doi.org/10.1103/PRXQuantum.3.030311Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCircuit quantum electrodynamicsCoulomb blockadeHybrid quantum systemsImpurities in superconductorsJosephson effectKondo effectLifetimes & widthsProximity effectQuantum phase transitionsSpin-singlet pairingPhysical SystemsJosephson junctionsNanowiresQuantum dotsSemiconductorsSuperconducting qubitsSuperconductorsTechniquesMicrowave techniquesNumerical Renormalization GroupCondensed Matter, Materials & Applied PhysicsQuantum Information

Universal time-domain Prony fitting decomposition for optimized hierarchical quantum master equations.

In this Communication, we propose the time-domain Prony fitting decomposition (t-PFD) as an accurate and efficient exponential series method, applicable to arbitrary bath correlation functions. The resulting numerical efficiency of hierarchical equations of motion (HEOM) formalism is greatly optimized, especially in low temperature regimes that would be inaccessible with other methods. For demonstration, we calibrate the present t-PFD against the celebrated Padé spectrum decomposition method, followed by converged HEOM evaluations on the single-impurity Anderson model system.

Dual Kondo effect charge ordering and zero thermal expansion in a correlated intermetallic

The possibility that valency changes due to the Kondo effect induce a charge-density-wave (CDW) transition and lead to zero-thermal-expansion by compensating the accompanying structural changes is appealing from both a fundamental and applied physics perspective. Theoretical studies have predicted CDW-order caused by the Kondo effect, whereby a material would exhibit a temperature-dependent dual Kondo effect comprising of two sublattices with different single-ion Kondo temperatures, but its experimental realization remains elusive. Here, we show direct evidence of a dual Kondo effect providing the electronic energy gain for a CDW accompanied by zero-thermal-expansion, in a strongly correlated f-electron material. YbPd undergoes a cubic to tetragonal transition with an incommensurate-CDW below T1 = 130 K, which becomes commensurate below T2 = 105 K. Bulk-sensitive spectroscopy reveals temperature-independent ytterbium single-site mixed-valence above T1, and a clear temperature-dependent mixed-valence charge-disproportionation of two crystallographic ytterbium sites in the CDW phases. Simplified single-impurity Anderson model calculations prove existence of a dual Kondo mixed-valency coupled to the CDW changes associated with the two ytterbium sites, and quantify site-dependent single-ion Kondo temperatures. The dual Kondo temperatures track the evolution of lattice parameters, resulting in a cell-volume compensated Kondo-CDW phase. The results provide a route to develop room temperature intermetallic zero-thermal-expansion materials.

Renormalization group for open quantum systems using environment temperature as flow parameter

We present the T-flow renormalization group method, which computes the memory kernel for the density-operator evolution of an open quantum system by lowering the physical temperature T of its environment. This has the key advantage that it can be formulated directly in real time, making it particularly suitable for transient dynamics, while automatically accumulating the full temperature dependence of transport quantities. We solve the T-flow equations numerically for the example of the single impurity Anderson model. We benchmark in the stationary limit, readily accessible in real-time for voltages on the order of the coupling or larger using results obtained by the functional renormalization group, density-matrix renormalization group and the quantum Monte Carlo method. Here we find quantitative agreement even in the worst case of strong interactions and low temperatures, indicating the reliability of the method. For transient charge currents we find good agreement with results obtained by the 2PI Green's function approach. Furthermore, we analytically show that the short-time dynamics of both local and non-local observables follow a "universal" temperature-independent behaviour when the metallic reservoirs have a flat wide band.

Feynman-Vernon influence functional approach to quantum transport in interacting nanojunctions: An analytical hierarchical study

We present a nonperturbative and formally exact approach for the charge transport in interacting nanojunctions based on a real-time path-integral formulation of the reduced system dynamics. For reservoirs of noninteracting fermions, the exact trace over the leads' degrees of freedom results in the time-nonlocal Feynman-Vernon influence functional, a functional of the Grassmann-valued paths of the nanojunction, which induces correlations among the tunneling transitions in and out of the nanojunction. An expansion of the influence functional in terms of the number of tunneling transitions, and integration of the Grassmann variables between the tunneling times, allows us to obtain a still exact generalized master equation for the populations of the reduced density matrix in the occupation-number representation, as well as a formally exact expression for the current. By borrowing the nomenclature of the famous spin-boson model, we parametrize the two-state dynamics of each single-particle fermionic degree of freedom, in the occupation-number representation, in terms of blips and sojourns. We apply our formalism to the exactly solvable resonant level model (RLM) and to the single-impurity Anderson model (SIAM), the latter being a prototype system for studying strong correlations. For both systems, we demonstrate a hierarchical diagrammatic structure. While the hierarchy closes at the second tier for the RLM, this is not the case for the interacting SIAM. Upon inspection of the current kernel, known results from various perturbative and nonperturbative approximation schemes to quantum transport in the SIAM are recovered. Finally, a noncrossing approximation for the hierarchical kernel is developed, which enables us to systematically decrease temperature at each next level of the approximation. Analytical results for a simplified fourth-tier scheme are presented both in equilibrium and nonequilibrium and with an applied magnetic field.

Hydrogen ion scattering from alkali/graphene surface: Alkali core states effects

We present a theoretical study of the frontal collision of protons with a graphene surface to which an alkali-adatom is added. Na and Cs adsorbates are studied in a low coverage limit. We analyze how the presence of adsorbates affects the charge exchange when the binary collision between the H+ protons and the adatoms or different carbon atoms close to the impurity occurs. The charge transfer process in the scattering of protons in the K and C atoms of a graphene surface to which a K adatom is added has already been analyzed and discussed in our previous works. We find that the inner states of the alkali atoms adsorbed on graphene introduce important differences in the charge transfer depending on their positions with respect to the valence band of graphene. For a better grasp of this, in this work we select Cs and Na as adatoms due to Cs has core levels that can resonate with the valence band of graphene, while Na does not. The interacting system is described by the Anderson Hamiltonian which takes into account the electronic repulsion at the projectile site; the ion charge fractions after the collision are calculated by using the non-equilibrium Green-Keldysh functions formalism. Also, we describe the adsorption of the alkali atom on the surface using the single impurity Anderson model and introduce the Green's functions required to calculate the adatom spectral density. In the scattering of H+ from Cs, the charge fractions as a function of the incident energy, behave similarly to the scattering from K. For the Na adatom, the dependence is different, showing a monotonous increase in the high energy regime. The results of this work allow us to infer the signals in the charge exchange, from the localized features of the density of states on the alkaline adsorbate during the scattering process, due to the peculiarities of the electronic band structure of graphene.

Kondo cloud in a one-dimensional nanowire

A recent experiment [Nature (London) 579, 210 (2020)] probed the extent of the Kondo cloud in 1D by measuring the effect of electrostatic perturbations applied a distance $L$ away from the impurity on ${T}_{K}$. We study the Kondo cloud in a model proposed to describe this experimental setup, consisting of a single impurity Anderson model coupled to two semi-infinite 1D leads. In agreement with the experimental results, we find that ${T}_{K}$ is strongly affected by perturbations to the lead within the Kondo cloud. We obtain a complementary picture of the Kondo cloud in this system by observing how the Kondo state manifests itself in the local density of states of the leads, which may be observed experimentally via scanning tunneling microscopy. Our results support the existing experimental data and provide detailed predictions for future experiments seeking to characterize the Kondo cloud in this system.