Impurity Model Research Articles

Current-induced forces in nanosystems: A hierarchical equations of motion approach

An approach to calculating current-induced forces in charge transport through nanosystems is introduced. Starting from the fully quantum mechanical hierarchical equations of motion formalism, a timescale separation between electronic and vibrational degrees of freedom is used to derive a classical Langevin equation of motion for the vibrational dynamics as influenced by current-induced forces, such as the electronic friction. The resulting form of the friction is shown to be equivalent to previously derived expressions. The numerical exactness of the hierarchical equations of motion approach, however, allows the investigation of transport scenarios with strong intrasystem and system-environment interactions. As a demonstration, the electronic friction of three example systems is calculated and analyzed: a single electronic level coupled to one classical vibrational mode, an Anderson impurity model coupled to one classical vibrational mode, and a single electronic level coupled to both a classical and quantum vibrational mode.

Control of Yu-Shiba-Rusinov States through a Bosonic Mode

We investigate the impact of a bosonic degree of freedom on Yu-Shiba-Rusinov states emerging from a magnetic impurity in a conventional superconductor. Starting from the Anderson impurity model, we predict that an additional p-wave conduction band channel opens up if a bosonic mode is coupled to the tunneling between impurity and host, which implies an additional pair of odd-parity Yu-Shiba-Rusinov states. The bosonic mode can be a vibrational mode or the electromagnetic field in a cavity. The exchange couplings in the two channels depend sensitively on the state of the bosonic mode (ground state, few quanta, or classically driven Floquet state), which opens possibilities for phononics or photonics control of such systems, with a rich variety of ground and excited states.

Dynamical Screening of Local Spin Moments at Metal–Molecule Interfaces

Transition-metal phthalocyanine molecules have attracted considerable interest in the context of spintronics device development due to their amenability to diverse bonding regimes and their intrinsic magnetism. The latter is highly influenced by the quantum fluctuations that arise at the inevitable metal-molecule interface in a device architecture. In this study, we have systematically investigated the dynamical screening effects in phthalocyanine molecules hosting a series of transition-metal ions (Ti, V, Cr, Mn, Fe, Co, and Ni) in contact with the Cu(111) surface. Using comprehensive density functional theory plus Anderson's Impurity Model calculations, we show that the orbital-dependent hybridization and electron correlation together result in strong charge and spin fluctuations. While the instantaneous spin moments of the transition-metal ions are near atomic-like, we find that screening gives rise to considerable lowering or even quenching of these. Our results highlight the importance of quantum fluctuations in metal-contacted molecular devices, which may influence the results obtained from theoretical or experimental probes, depending on their possibly material-dependent characteristic sampling time-scales.

Real-time evolution of Anderson impurity models via tensor network influence functionals

In this work we present and analyze two tensor network-based influence functional approaches for simulating the real-time dynamics of quantum impurity models such as the Anderson model. Via comparison with recent numerically exact simulations, we show that such methods accurately capture the long-time non-equilibrium quench dynamics. The two parameters that must be controlled in these tensor network influence functional approaches are a time discretization (Trotter) error and a bond dimension (tensor network truncation) error. We show that the actual numerical uncertainties are controlled by an intricate interplay of these two approximations which we demonstrate in different regimes. Our work opens the door to using these tensor network influence functional methods as general impurity solvers.

Solving Anderson Impurity Model by the Effective Hamiltonian Theory

We apply the Self-Consistent Effective Hamiltonian Theory (SCEHT), which uses a general variational Fermionic many-body wave function to generate an effective Hamiltonian in a quadratic form, to the Anderson impurity model. The chiral symmetry-breaking quadratic effective Hamiltonian is solved exactly for the single Fermion excitation spectrum. We validate the theory by numerically solving a model problem. The solution shows the correct Kondo resonance in the quasi-particle density of states.

Itinerant-localized dichotomy in magnetic anisotropic properties of U-based ferromagnets

The electronic structure, spin and orbital magnetic moments, and the magnetic anisotropy energy in selected U-based compounds are investigated making use of the correlated band theory. First, we demonstrate that the LSDA+U approach with exact atomic limit implemented as a combination of the relativistic density functional theory with the Anderson impurity model provides a good quantitative description for UGa{}_2. Further, the method is applied to UFe_{12} and UFe{}_{10}Si{}_2 ferromagnets. The calculated positive uniaxial magnetic anisotropy together with negative enthalpy of formation for UFe{}_{10}Si{}_2 make it as a candidate for the magnetically hard materials. Our studies suggest a viable route for further development of the rare-earth-lean permanent magnets by replacing a part of U atoms by some rare-earth like Sm in UFe{}_{10}Si{}_2.

Configuration interaction based nonequilibrium steady state impurity solver

We present a solver for correlated impurity problems out of equilibrium based on a combination of the so-called auxiliary master equation approach (AMEA) and the configuration interaction expansion. Within AMEA one maps the original impurity model onto an auxiliary open quantum system with a restricted number of bath sites which can be addressed by numerical many-body approaches such as Lanczos/Arnoldi exact diagonalization (ED) or matrix product states (MPS). While the mapping becomes exponentially more accurate with increasing number of bath sites, ED implementations are severely limited due to the fast increase of the Hilbert space dimension for open systems, and the MPS solver typically requires rather long runtimes. Here, we propose to adopt a configuration interaction approach augmented by active space extension to solve numerically the correlated auxiliary open quantum system. This allows access to a larger number of bath sites at lower computational costs than for plain ED. We benchmark the approach with numerical renormalization group results in equilibrium and with MPS out of equilibrium. In particular, we evaluate the current, the conductance, as well as the Kondo peak and its splitting as a function of increasing bias voltage below the Kondo temperature ${T}_{\text{K}}$. We obtain a rather accurate scaling of the conductance as a function of the bias voltage and temperature rescaled by ${T}_{\text{K}}$ for moderate to strong interactions in a wide range of parameters. The approach combines the fast runtime of ED with an accuracy close to the one achieved by MPS making it an attractive solver for nonequilibrium dynamical mean field theory.

Quantum effects of solitons in the self-dual impurity model

We compute the vacuum polarization energies (VPE) of solitons in a self-dual impurity model in which the soliton profiles take the shape of a separated kink-antikink pair. Classically the soliton energies are invariant under the change of a continuous parameter that can be interpreted as the kink-antikink separation. This is not the case for the VPE so that quantum effects decide on the energetically most favorable separation. The considered configurations are classically stable so that its quantum fluctuations have only real frequency eigenvalues. Hence, in contrast to the kink-antikink configuration in the $\phi^4$ model, the VPE is well defined for any value of the separation and we gain insight into the quantum corrections to the kink-antikink potential

Single- and Multimagnon Dynamics in Antiferromagnetic α−Fe2O3 Thin Films

Understanding the spin dynamics in antiferromagnetic (AFM) thin films is fundamental for designing novel devices based on AFM magnon transport. Here, we study the magnon dynamics in thin films of AFM $S=5/2$ $\alpha$-Fe$_2$O$_3$ by combining resonant inelastic x-ray scattering, Anderson impurity model plus dynamical mean-field theory, and Heisenberg spin model. Below 100 meV, we observe the thickness-independent (down to 15 nm) acoustic single-magnon mode. At higher energies (100-500 meV), an unexpected sequence of equally spaced, optical modes is resolved and ascribed to $\Delta S_z = 1$, 2, 3, 4, and 5 magnetic excitations corresponding to multiple, noninteracting magnons. Our study unveils the energy, character, and momentum-dependence of single and multimagnons in $\alpha$-Fe$_2$O$_3$ thin films, with impact on AFM magnon transport and its related phenomena. From a broader perspective, we generalize the use of L-edge resonant inelastic x-ray scattering as a multispin-excitation probe up to $\Delta S_z = 2S$. Our analysis identifies the spin-orbital mixing in the valence shell as the key element for accessing excitations beyond $\Delta S_z = 1$, and up to, e.g., $\Delta S_z = 5$. At the same time, we elucidate the novel origin of the spin excitations beyond the $\Delta S_z = 2$, emphasizing the key role played by the crystal lattice as a reservoir of angular momentum that complements the quanta carried by the absorbed and emitted photons.

Vertex-Based Diagrammatic Treatment of Light-Matter-Coupled Systems.

We propose a diagrammatic MonteCarlo approach for quantum impurity models, which can be regarded as a generalization of the strong-coupling expansion for fermionic impurity models. The algorithm is based on a self-consistently computed three-point vertex and a stochastically sampled four-point vertex, and it allows one to obtain numerically exact results in a wide parameter regime. The performance of the algorithm is demonstrated with applications to a spin-boson model representing an emitter in a waveguide. As a function of the coupling strength, the spin exhibits a delocalization-localization crossover at low temperatures, signaling a qualitative change in the real-time relaxation. In certain parameter regimes, the response functions of the emitter coupled to the electromagnetic continuum can be described by an effective Rabi model with appropriately defined parameters. We also discuss the spatial distribution of the photon density around the emitter.

Kondo nanomechanical dissipation in the driven Anderson impurity model

The cyclic sudden switch of a magnetic impurity from a Kondo to a non-Kondo state and back was recently proposed to involve an important dissipation of the order of several ${k}_{B}{T}_{K}$ per cycle. The possibility to reveal this and other electronic processes through nanomechanical dissipation by, e.g., ultrasensitive atomic force microscope (AFM) tools would represent an unusual and interesting form of spectroscopy. Here, we explore the dependence on the switching time of the expected dissipation, a quantity whose magnitude is physically expected to drop from maximum to zero between sudden and slow switching, respectively. As an application of a recently established matrix-product-state-based time-dependent variational algorithm, we study the magnetic-field-induced Kondo switching in an Anderson model of the magnetic impurity. We find, quite reasonably, that dissipation requires switching within the Kondo timescale $\ensuremath{\hbar}{({k}_{B}{T}_{K})}^{\ensuremath{-}1}$ or faster. While such a fast switching seems problematic for current AFM setups, the challenge remains open for future means to detect this dissipation by time-dependent magnetic fields, an electrostatic impurity level shift, or hybridization switching. The technical aspects revealed by this approach will be of interest for future nonequilibrium calculations.

Comparative study of adaptive variational quantum eigensolvers for multi-orbital impurity models

Hybrid quantum-classical embedding methods for correlated materials simulations provide a path towards potential quantum advantage. However, the required quantum resources arising from the multi-band nature of d and f electron materials remain largely unexplored. Here we compare the performance of different variational quantum eigensolvers in ground state preparation for interacting multi-orbital embedding impurity models, which is the computationally most demanding step in quantum embedding theories. Focusing on adaptive algorithms and models with 8 spin-orbitals, we show that state preparation with fidelities better than 99.9% can be achieved using about 214 shots per measurement circuit. When including gate noise, we observe that parameter optimizations can still be performed if the two-qubit gate error lies below 10−3, which is slightly smaller than current hardware levels. Finally, we measure the ground state energy on IBM and Quantinuum hardware using a converged adaptive ansatz and obtain a relative error of 0.7%.

Проблема формирования федоровских гончарных традиций в бронзовом веке Зауралья

Fyodorovka (Andronovo) ceramics is quite similar from the Transurals to the Minusinsk Basin, which suggests a single mechanism for its formation. The study of ceramics of the Mochishche settlement in the Transurals showed that typologically, Fyodorovka ware, as elsewhere, is different from the previous Alakul one and could not be formed on its basis. However, in pottery technologies the situation is more complicated. In the clay sources, silty clays, or ordinary non-sandy clays, were found, indicating the coming of the Fyodorovka people from the Lower Tobol region, but Alakul traditions are visible in the modeling of ware and impurities to clay. The formation of the Fyodorovka pottery traditions in the west was associated with the coming of the Fyodorovka people from the Altai to the Tobol region, and then to the Transurals, which mixed with the local Alakul people. But in the Altai, this was preceded by an impulse from the west, as a result of which elements of Petrovka-Alakul pottery were introduced there. It is also possible that there was a southern impulse from the area of the Bactria-Margiana archaeological complex (BMAC), and this is associated with the widespread use of chamotte tradition, although it is also known in Petrovka-Alakul pottery.

Spin-orbit coupling and Kondo resonance in the Co adatom on the Cu(100) surface: DFT plus exact diagonalization study

We report density functional theory plus exact diagonalization of the multiorbital Anderson impurity model calculations for the Co adatom on the top of a Cu(001) surface. For the Co atom $d$-shell occupation ${n}_{d}\ensuremath{\approx}8$, a singlet many-body ground state and Kondo resonance are found, when the spin-orbit coupling is included in the calculations. The differential conductance is evaluated in good agreement with the scanning tunneling microscopy measurements. The results illustrate the essential role which the spin-orbit coupling is playing in the formation of a Kondo singlet for the multiorbital impurity in low dimensions.

Evaluation of the reproducibility and positive controls of cellular immortality test for the detection of immortalized cellular impurities in human cell-processed therapeutic products.

Contamination of human cell-processed therapeutic products (hCTPs) with tumorigenic/immortalized cellular impurities is a major concern in the manufacturing and quality control of hCTPs. The cellular immortality test based on cell growth analysis is a method for detecting tumorigenic/immortalized cellular impurities in hCTPs. However, the performance of the cellular immortality test has not yet been well characterized. In this study, we examined the reproducibility of the cellular immortality test in detecting HeLa cells as a model of tumorigenic cellular impurities, as well as the applicability of other models of cellular impurities with different tumorigenicity to the cellular immortality test. Using HeLa cells as a model for cellular impurities, we measured the growth rate of human mesenchymal stem cells (hMSCs) supplemented with HeLa cells at concentrations ranging from 0.01 to 0.0001% at each passage in three laboratories and evaluated the reproducibility of the detection of immortalized cellular impurities. In addition, HEK293cells (another immortalized cell line) and MRC-5cells (a non-immortalized cell line) were employed as cellular impurity models that exhibit different growth characteristics from HeLa cells, and the ability of the cellular immortality test to detect these different impurities when mixed with hMSCs was examined. In the multisite study, the growth rate of hMSCs supplemented with 1 and 10 HeLa cells (0.0001% and 0.001%) significantly increased and reached a plateau in all three laboratories, whereas those of hMSCs alone eventually decreased. Moreover, when hMSCs were supplemented with 10 and 100 HEK293 and MRC-5cells (0.001% and 0.01%), the growth rate significantly increased. The growth rate of hMSCs supplemented with HEK293cells increased with passage and remained high, whereas that of hMSCs supplemented with MRC-5cells eventually decreased, as in the case of hMSCs alone. These results indicate that the cellular immortality test is reproducible and can detect immortalized (i.e., potentially tumorigenic) cells such as HEK293cells with a lower growth rate than HeLa cells by discriminating against normal cells, which could contribute to ensuring the safety and quality of hCTPs.

Cluster-mediated stop-and-go crystallization‬

Impurities control the formation of bio-crystals and can fully paralyze crystal growth at low levels of supersaturation. Traditional impurity models predict that an escape from this so-called “dead zone” requires an increase in the driving force (i.e. supersaturation). In this work, using protein crystals as a model system, we uncover an alternative escape route from the dead zone that does not involve an increase in supersaturation. We demonstrate that the merger of a protein cluster with the crystal surface triggers the formation of an ordered multi-layered island. The newly created surface on top of the resulting 3D island is initially devoid of impurities and therefore characterized by near-pure step growth kinetics. The accelerated step advancement on this relatively uncontaminated surface limits the available time for impurities to adsorb on the emerging terraces and by extension their resulting surface density. Cluster-mediated crystal growth occurring in heterogeneous media can therefore lead to stop-and-go dynamics, which offers a new model to explain crystallization taking place under biological control (e.g. biomineralization).

Satellites in the Ti 1s core level spectra of SrTiO3 and TiO2

Satellites in core level spectra of photoelectron spectroscopy (PES) can provide crucial information on the electronic structure and chemical bonding in materials, particular in transition metal oxides. This paper explores satellites of the Ti 1$s$ and 2$p$ core level spectra of SrTiO$_3$ and TiO$_2$. Conventionally, soft x-ray PES (SXPS) probes the Ti 2$p$ core level; however, it is not ideal to fully capture satellite features due to its inherent spin-orbit-splitting (SOS). Here, hard x-ray PES(HAXPES) provides access to the Ti 1$s$ spectrum instead, which allows us to study intrinsic charge responses upon core-hole creation without the complication from SOS and with favorable intrinsic linewidths. The experimental spectra are theoretically analyzed by two impurity models, including an Anderson impurity model (AIM) built on local density approximation (LDA) and dynamical mean-field theory (DMFT), and a conventional TiO$_6$ cluster model. The theoretical results emphasize the importance of explicit inclusion of higher-order Ti-O charge-transfer processes beyond the nearest-neighboring Ti-O bond to simulate the core level spectra of SrTiO$_3$ and TiO$_2$. The AIM approach with continuous bath orbitals provided by LDA+DMFT represents the experimental spectra well. Crucially, with the aid of the LDA+DMFT method, this paper provides a robust prescription of how to use the computationally cheap cluster model in fitting analyses of core level spectra.

Effect of realistic out-of-plane dopant potentials on the superfluid density of overdoped cuprates

Recent experimental papers on hole-doped overdoped cuprates have argued that a series of observations showing unexpected behavior in the superconducting state imply the breakdown of the quasiparticle-based Landau-BCS paradigm in that doping range. In contrast, some of the present authors have argued that a phenomenological "dirty $d$-wave" theoretical analysis explains essentially all aspects of thermodynamic and transport properties in the superconducting state, provided the unusual effects of weak, out-of-plane dopant impurities are properly accounted for. Here we attempt to place this theory on a more quantitative basis by performing $\textit{ab-initio}$ calculations of dopant impurity potentials for LSCO and Tl-2201. These potentials are more complex than the pointlike impurity models considered previously, and require calculation of forward scattering corrections to transport properties. Including realistic, ARPES-derived bandstructures, Fermi liquid renormalizations, and vertex corrections, we show that the theory can explain semiquantitatively the unusual superfluid density measurements of the two most studied overdoped materials.

Aubry-André Anderson model: Magnetic impurities coupled to a fractal spectrum

The Anderson model for a magnetic impurity in a one-dimensional quasicrystal is studied using the numerical renormalization group (NRG). The main focus is elucidating the physics at the critical point of the Aubry-Andre (AA) Hamiltonian, which exhibits a fractal spectrum with multifractal wave functions, leading to an AA Anderson (AAA) impurity model with an energy-dependent hybridization function defined through the multifractal local density of states at the impurity site. We first study a class of Anderson impurity models with uniform fractal hybridization functions that the NRG can solve to arbitrarily low temperatures. Below a Kondo scale $T_K$, these models approach a fractal strong-coupling fixed point where impurity thermodynamic properties oscillate with $\log_b T$ about negative average values determined by the fractal dimension of the spectrum. The fractal dimension also enters into a power-law dependence of $T_K$ on the Kondo exchange coupling $J_K$. To treat the AAA model, we combine the NRG with the kernel polynomial method (KPM) to form an efficient approach that can treat hosts without translational symmetry down to a temperature scale set by the KPM expansion order. The aforementioned fractal strong-coupling fixed point is reached by the critical AAA model in a simplified treatment that neglects the wave-function contribution to the hybridization. The temperature-averaged properties are those expected for the numerically determined fractal dimension of $0.5$. At the AA critical point, impurity thermodynamic properties become negative and oscillatory. Under sample-averaging, the mean and median Kondo temperatures exhibit power-law dependences on $J_K$ with exponents characteristic of different fractal dimensions. We attribute these signatures to the impurity probing a distribution of fractal strong-coupling fixed points with decreasing temperature.

Interplay of charge and spin fluctuations in a Hund's coupled impurity

In Hund's metals, the local ferromagnetic interaction between orbitals leads to an emergence of complex electronic states with large and slowly fluctuating magnetic moments. Introducing the Hund's coupled mixed valence quantum impurity, we gain analytic insight into recent numerical renormalization group studies. We show that valence fluctuations drastically impede the development of a large fluctuating moment over a wide range of temperatures and energy, characterized by quenched orbital degrees of freedom and a singular logarithmic behavior of the spin susceptibility $\chi_{\rm sp}''(\omega) \propto [\omega \ln(\omega/T_K^{\rm eff})^2]^{-1}$, closely resembling power-law scaling $\chi_{\rm sp}''(\omega) \sim \omega^{-\gamma}$. Such singular spin fluctuations are suspected to play an important role in future models of Hund's driven Cooper pairing.