Single-impurity Anderson Model Research Articles

Extracting dynamical maps of non-Markovian open quantum systems.

The most general description of quantum evolution up to a time τ is a completely positive tracing preserving map known as a dynamical mapΛ̂(τ). Here, we consider Λ̂(τ) arising from suddenly coupling a system to one or more thermal baths with a strength that is neither weak nor strong. Given no clear separation of characteristic system/bath time scales, Λ̂(τ) is generically expected to be non-Markovian; however, we do assume the ensuing dynamics has a unique steady state, implying the baths possess a finite memory time τm. By combining several techniques within a tensor network framework, we directly and accurately extract Λ̂(τ) for a small number of interacting fermionic modes coupled to infinite non-interacting Fermi baths. First, we use an orthogonal polynomial mapping and thermofield doubling to arrive at a purified chain representation of the baths whose length directly equates to a time over which the dynamics of the infinite baths is faithfully captured. Second, we employ the Choi-Jamiolkowski isomorphism so that Λ̂(τ) can be fully reconstructed from a single pure state calculation of the unitary dynamics of the system, bath and their replica auxiliary modes up to time τ. From Λ̂(τ), we also compute the time local propagator L̂(τ). By examining the convergence with τ of the instantaneous fixed points of these objects, we establish their respective memory times τmΛ and τmL. Beyond these times, the propagator L̂(τ) and dynamical map Λ̂(τ) accurately describe all the subsequent long-time relaxation dynamics up to stationarity. These timescales form a hierarchy τmL≤τmΛ≤τre, where τre is a characteristic relaxation time of the dynamics. Our numerical examples of interacting spinless Fermi chains and the single impurity Anderson model demonstrate regimes where τre ≫ τm, where our approach can offer a significant speedup in determining the stationary state compared to directly simulating the long-time limit. Our results also show that having access to Λ̂(τ) affords a number of insightful analyses of the open system thus far not commonly exploited.

Self-Consistent Determination of Single-Impurity Anderson Model Using Hybrid Quantum-Classical Approach on a Spin Quantum Simulator.

The accurate determination of the electronic structure of strongly correlated materials using first principle methods is of paramount importance in condensed matter physics, computational chemistry, and material science. However, due to the exponential scaling of computational resources, incorporating such materials into classical computation frameworks becomes prohibitively expensive. In 2016, Bauer etal. proposed a hybrid quantum-classical approach to correlated materials [B. Bauer et al., Hybrid quantum-classical approach to correlated materials, Phys. Rev. X 6, 031045 (2016).PRXHAE2160-330810.1103/PhysRevX.6.031045] that can efficiently tackle the electronic structure of complex correlated materials. Here, we experimentally demonstrate that approach to tackle the computational challenges associated with strongly correlated materials. By seamlessly integrating quantum computation into classical computers, we address the most computationally demanding aspect of the calculation, namely the computation of the Green's function, using a spin quantum processor. Furthermore, we realize a self-consistent determination of the single impurity Anderson model through a feedback loop between quantum and classical computations. A quantum phase transition in the Hubbard model from the metallic phase to the Mott insulator is observed as the strength of electron correlation increases. As the number of qubits with high control fidelity continues to grow, our experimental findings pave the way for solving even more complex models, such as strongly correlated crystalline materials or intricate molecules.

Universality and the thermoelectric transport properties of a double quantum dot system: Seeking for conditions that improve the thermoelectric efficiency

Employing universal relations for the Onsager coefficients in the linear regime at the symmetric point of the single impurity Anderson model, we calculate the conditions under which the quantum scattering phase shift should satisfy to produce the asymptotic Carnot’s limit for the thermoelectric efficiency. We show that a single quantum dot connected by metallic leads at the Kondo regime cannot achieve the best thermoelectric efficiency. We study a serial double quantum dot system, with the quantum dots immersed in ballistic conduction channels. Each QD exhibits a strong but finite local electronic correlation UU. We show that maintaining one dot in the electron-hole symmetric point and allowing charge fluctuations in the other QD makes it possible to drive the system to the maximum thermoelectric efficiency. We also show that the bound states in the continuum (BICs) and quasi-BICs associated with the quantum scattering interference process drive the DQD to the maximum thermoelectric efficiency. We identify two types of quasi-BICs that occur at low and high temperatures: The first is associated with single Fano resonances, and the last is with several Fano processes. We also discussed possible temperature values and conditions that could be linked with the experimental realization of the results.

KeldyshQFT: A C++ codebase for real-frequency multiloop functional renormalization group and parquet computations of the single-impurity Anderson model.

We provide a detailed exposition of our computational framework designed for the accurate calculation of real-frequency dynamical correlation functions of the single-impurity Anderson model in the regime of weak to intermediate coupling. Using quantum field theory within the Keldysh formalism to directly access the self-energy and dynamical susceptibilities in real frequencies, as detailed in our recent publication [Ge et al., Phys. Rev. B 109, 115128 (2024)], the primary computational challenge is the full three-dimensional real-frequency dependence of the four-point vertex. Our codebase provides a fully MPI+OpenMP parallelized implementation of the functional renormalization group (fRG) and the self-consistent parquet equations within the parquet approximation. It leverages vectorization to handle the additional complexity imposed by the Keldysh formalism, using optimized data structures and highly performant integration routines. Going beyond the results shown in the previous publication, the code includes functionality to perform fRG calculations in the multiloop framework, up to arbitrary loop order, including self-consistent self-energy iterations. Moreover, implementations of various regulators, such as hybridization, interaction, frequency, and temperature, are supplied.

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.