Impurity Model Research Articles

Optimization of chemical engineering control for large-scale alkaline electrolysis systems based on renewable energy sources

In the context of renewable energy, dynamic control is crucial for large-scale alkaline water electrolysis systems. Under traditional Proportional-Integral-Derivative (PID) control, the system's temperature and impurity levels may exceed safe limits during sudden load changes, compromising system safety. Therefore, this study proposes a control strategy based on mathematical models of system temperature and impurities, including Model Predictive Control (MPC) for temperature and Optimal Curve Tracking (OCT) for impurities. The MPC controller offsets the disturbances in temperature caused by current fluctuations through state prediction, while the OCT controller ensures that impurity levels remain within safe limits. Real-time application of these control strategies is achieved through MATLAB-PLC communication, validating controller performance. Experimental results show that the MPC controller exhibits excellent dynamic response and stability in controlling the stack temperature, with a maximum temperature peak deviation of only 2.9 K and a temperature fluctuation range of 5.9 K. This represents a reduction of 1.6 K in peak deviation compared to traditional PID controllers and significantly decreases the temperature fluctuation range. The OCT controller also demonstrates good safety and stability in controlling hydrogen to oxygen (HTO) impurity levels, consistently maintaining the HTO content at the set upper limit of 1.5%, thereby expanding the safe operational range of the system and reducing the need for frequent adjustments to the system setpoints.

Nonequilibrium steady state full counting statistics in the noncrossing approximation.

Quantum transport is often characterized not just by mean observables like the particle or energy current but by their fluctuations and higher moments, which can act as detailed probes of the physical mechanisms at play. However, relatively few theoretical methods are able to access the full counting statistics (FCS) of transport processes through electronic junctions in strongly correlated regimes. While most experiments are concerned with steady state properties, most accurate theoretical methods rely on computationally expensive propagation from a tractable initial state. Here, we propose a simple approach for computing the FCS through a junction directly at the steady state, utilizing the propagator noncrossing approximation. Compared to time propagation, our method offers reduced computational cost at the same level of approximation, but the idea can also be used within other approximations or as a basis for numerically exact techniques. We demonstrate the method's capabilities by investigating the impact of lead dimensionality on electronic transport in the nonequilibrium Anderson impurity model at the onset of Kondo physics. Our results reveal a distinct signature of one dimensional leads in the noise and Fano factor not present for other dimensionalities, showing the potential of FCS measurements as a probe of the environment surrounding a quantum dot.

Review of Yu–Shiba–Rusinov bound state in quantum impurity structures: basic principle and current progress

Abstract Magnetic impurities connected to superconductors reservoir result in bound states within the superconducting gap, so called Yu–Shiba–Rusinov (YSR) state. In the past few years, this field has gained much attention since it is crucial for engineering novel superconducting many-body states, with the perspective of manufacturing Majorana Fermions. The underlying physical picture of YSR state depends closely on the form of the impurities connected to the leads, the manner in which the impurities are organized, and also the diverse local interactions, which is always disclosed with the aid of quantum impurity models. This article provides a comprehensive overview of the progress achieved by previous studies, focusing on the issues demonstrated by quantum impurity structures. The physical mechanisms and the related phenomena assisted by different interactions are discussed in detail. Furthermore, a comprehensive overview of recent experimental achievements is presented, using various metal phthalocyanine molecules as illustrative examples, thereby establishing a robust foundation for future inquiries in this domain.

Geometrical perspective on spin-lattice density-functional theory.

A recently developed viewpoint on the fundamentals of density-functional theory for finite interacting spin-lattice systems that centers around the notion of degeneracy regions is presented. It allows for an entirely geometrical description of the Hohenberg-Kohn theorem and v-representability. The phenomena receive exemplification by an Anderson impurity model and other small-lattice examples. The case of adiabatic change and the time-dependent setting are examined as well.

Grassmann time-evolving matrix product operators: An efficient numerical approach for fermionic path integral simulations.

Developing numerical exact solvers for open quantum systems is a challenging task due to the non-perturbative and non-Markovian nature when coupling to structured environments. The Feynman-Vernon influence functional approach is a powerful analytical tool to study the dynamics of open quantum systems. Numerical treatments of the influence functional including the quasi-adiabatic propagator technique and the tensor-network-based time-evolving matrix product operator method have proven to be efficient in studying open quantum systems with bosonic environments. However, the numerical implementation of the fermionic path integral suffers from the Grassmann algebra involved. In this work, we present a detailed introduction to the Grassmann time-evolving matrix product operator method for fermionic open quantum systems. In particular, we introduce the concepts of Grassmann tensor, signed matrix product operator, and Grassmann matrix product state to handle the Grassmann path integral. Using the single-orbital Anderson impurity model as an example, we review the numerical benchmarks for structured fermionic environments for real-time nonequilibrium dynamics, real-time and imaginary-time equilibration dynamics, and its application as an impurity solver. These benchmarks show that our method is a robust and promising numerical approach to study strong coupling physics and non-Markovian dynamics. It can also serve as an alternative impurity solver to study strongly correlated quantum matter with dynamical mean-field theory.

Study on the mechanism of laser-induced breakdown and damage performance of internal defects in transparent materials through local optical field modulation

This paper establishes a photothermal damage model for bubble impurities affecting laser optical field modulation based on Mie scattering theory and incorporates the effects of optical field modulation. This model elucidates the evolution mechanism of synergistic damage in fused silica, with simulation results validated through experimental verification. A novel characterization of optical breakdown due to bubble impurities is proposed, occurring on a millisecond timescale through the dynamic evolution of combustion waves. The model delineates the influence of bubble size and spacing on optical field distribution, temperature, stress distribution, and their evolutionary behaviors. The modulation of the optical field due to double bubble impurities creates a localized “hot spot,” resulting in a differential transverse contraction stress at the edges of the bubble impurities, thereby reducing the damage threshold of fused silica. The spacing of 1.1 λ represents the enhancement node for optical field modulation by double bubble impurities. Furthermore, localized oscillations in the optical field arise when the spacing between the double bubbles exceeds 1.1 λ, attributed to changes in the refractive index at the bubble defects and resonance oscillations generated by optical field modulation. This study not only enhances our understanding of the optical field modulation processes occurring at 1064 nm in the presence of bubble defects but also establishes a theoretical foundation for detecting internal defects at this wavelength without inducing surface damage.

Quantifying the quantum nature of high-spin YSR excitations in transverse magnetic field.

Excitations of individual and coupled spins on superconductors provide a platform to study quantum spin impurity models as well as a pathway toward realizing topological quantum computing. Here, we characterize, using ultralow temperature scanning tunneling microscopy/spectroscopy, the Yu-Shiba-Rusinov (YSR) states of individual manganese phthalocyanine molecules with high spin on an ultrathin lead film in variable transverse magnetic field. We observe two types of YSR excitations, depending on the adsorption geometry. Using a zero-bandwidth model, we detail the role of the magnetic anisotropy, spin-spin exchange, and Kondo exchange. We illustrate that one molecular type can be treated as an individual spin, whereas the other type is best described by a coupled spin system. Using the field dependence of the YSR excitations combined with modeling, we describe the quantum phase of each excitation type. These results provide an insight into the quantum nature of YSR excitations in magnetic field and a platform to study spin impurity models on superconductors in magnetic field.

Unsupervised learning of effective quantum impurity models

Generalized quantum impurity models—which feature a few localized and strongly correlated degrees of freedom coupled to itinerant conduction electrons—describe diverse physical systems, from magnetic moments in metals to nanoelectronics quantum devices such as quantum dots or single-molecule transistors. Correlated materials can also be understood as self-consistent impurity models through dynamical mean-field theory. Accurate simulation of such models is challenging, especially at low temperatures, due to many-body effects from electronic interactions, resulting in strong renormalization. In particular, the interplay between local impurity complexity and Kondo physics is highly nontrivial. A common approach, which we further develop in this work, is to consider instead a simpler effective impurity model that still captures the low-energy physics of interest. The mapping from a bare to an effective model is typically done perturbatively, but even this can be difficult for complex systems, and the resulting effective model parameters can nevertheless be quite inaccurate. Here we develop a nonperturbative, unsupervised machine learning approach to systematically obtain low-energy effective impurity-type models, based on the renormalization-group framework. The method is shown to be general and flexible, as well as accurate and systematically improvable. We benchmark the method against exact results for the Anderson impurity model, and we provide an outlook for more complex models beyond the reach of existing methods. Published by the American Physical Society 2024

Mpsqd: A matrix product state based Python package to simulate closed and open system quantum dynamics.

We introduce a Python package based on matrix product states (MPS) to simulate both the time-dependent Schrödinger equation (TDSE) and the hierarchical equations of motion (HEOM). The wave function in the TDSE or the reduced density operator/auxiliary density operators in the HEOM are represented using MPS. A matrix product operator (MPO) is then constructed to represent the Hamiltonian in the TDSE or the generalized Liouvillian in the HEOM. The fourth-order Runge-Kutta method and the time-dependent variational principle are used to propagate the MPS. Several examples, including the nonadiabatic interconversion dynamics of the pyrazine molecule, excitation energy transfer dynamics in molecular aggregates and photosynthetic light-harvesting complexes, the spin-boson model, a laser driven two-state model, the Holstein model, and charge transport in the Anderson impurity model, are presented to demonstrate the capability of the package.

Inchworm quasi Monte Carlo for quantum impurities

The inchworm expansion is a promising approach to solving strongly correlated quantum impurity models due to its reduction of the sign problem in real and imaginary time. However, inchworm Monte Carlo is computationally expensive, converging as 1/N where N is the number of samples. We show that the imaginary-time integration is amenable to quasi Monte Carlo, with parametrically better 1/N convergence, by mapping the Sobol low-discrepancy sequence from the hypercube to the simplex with the so-called Root transform. This extends the applicability of the inchworm method to, e.g., multiorbital Anderson impurity models with off-diagonal hybridization, relevant for materials simulation, where continuous-time hybridization expansion Monte Carlo has a severe sign problem. Published by the American Physical Society 2024

Vacancy-Induced Tunable Kondo Effect in Twisted Bilayer Graphene.

In single sheets of graphene, vacancy-induced states have been shown to host an effective spin-1/2 hole that can be Kondo screened at low temperatures. Here, we show how these vacancy-induced impurity states survive in twisted bilayer graphene (TBG), which thus provides a tunable system to probe the critical destruction of the Kondo effect in pseudogap hosts. Abinitio calculations and atomic-scale modeling are used to determine the nature of the vacancy states in the vicinity of the magic angle in TBG, demonstrating that the vacancy can be treated as a quantum impurity. Utilizing this insight, we construct an Anderson impurity model with a TBG host that we solve using the numerical renormalization group combined with the kernel polynomial method. We determine the phase diagram of the model and show how there is a strict dichotomy between vacancies in the AA/BB versus AB/BA tunneling regions. In AB/BA vacancies, the Kondo temperature at the magic angle develops a broad distribution with a tail to vanishing temperatures due to multifractal wave functions at the magic angle. We argue that scanning tunneling microscopy in the vicinity of the vacancy can act as a probe of both the critical single-particle states and the underlying many-body ground state in magic-angle TBG.

Prerelaxation in quantum, classical, and quantum-classical two-impurity models

We numerically study the relaxation dynamics of impurity-host systems, focusing on the presence of long-lived metastable states in the nonequilibrium dynamics after an initial excitation of the impurities. In generic systems, an excited impurity coupled to a large bath at zero temperature is expected to relax and approach its ground state over time. However, certain exceptional cases exhibit metastability, where the system remains in an excited state on timescales largely exceeding the typical relaxation time. We study this phenomenon for three prototypical impurity models: a tight-binding quantum model of independent spinless fermions on a lattice with two stub impurities, a classical-spin Heisenberg model with two weakly coupled classical impurity spins, and a tight-binding quantum model of independent electrons with two classical impurity spins. Through numerical integration of the fundamental equations of motion, we find that all three models exhibit similar qualitative behavior: complete relaxation for nearest-neighbor impurities and incomplete or strongly delayed relaxation for next-nearest-neighbor impurities. The underlying mechanisms leading to this behavior differ between models and include impurity-induced bound states, emergent approximately conserved local observables, and exact cancellation of local and nonlocal dissipation effects. Published by the American Physical Society 2024

Simplicial models for the epistemic logic of faulty agents

In recent years, several authors have been investigating simplicial models, a model of epistemic logic based on higher dimensional structures called simplicial complexes. In the original formulation of Goubault et al. (Inf Comput 278:104597, 2021. https://doi.org/10.1016/j.ic.2020.104597), simplicial models are always assumed to be pure, meaning that all worlds have the same dimension. This is equivalent to the standard S5n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbf {S5_n}$$\\end{document} semantics of epistemic logic, based on Kripke models. By removing the assumption that models must be pure, we can go beyond the usual Kripke semantics and study epistemic logics where the number of agents participating in a world can vary. This approach has been developed in a number of papers (van Ditmarsch, WoLLIC 2021, pp 31–46, 2021. https://doi.org/10.1007/978-3-030-88853-4_3; Goubault et al. STACS 2022, pp 33:1–33:20, 2022. https://doi.org/10.4230/LIPIcs.STACS.2022.33; Goubault et al. LICS, pp 1–13, 2023. https://doi.org/10.1109/LICS56636.2023.10175737), with applications in fault-tolerant distributed computing where processes may crash during the execution of a system. A difficulty that arises is that subtle design choices in the definition of impure simplicial models can result in different axioms of the resulting logic. In this paper, we classify those design choices systematically, and axiomatize the corresponding logics. We illustrate them via distributed computing examples of synchronous systems where processes may crash.

Steady-state properties of multi-orbital systems using quantum Monte Carlo.

A precise dynamical characterization of quantum impurity models with multiple interacting orbitals is challenging. In quantum Monte Carlo methods, this is embodied by signproblems. A dynamical signproblem makes it exponentially difficult to simulate long times. A multi-orbital signproblem generally results in a prohibitive computational cost for systems with multiple impurity degrees of freedom even in static equilibrium calculations. Here, we present a numerically exact inchworm method that simultaneously alleviates both signproblems, enabling simulation of multi-orbital systems directly in the equilibrium or nonequilibrium steady-state. The method combines ideas from the recently developed steady-state inchworm Monte Carlo framework [Erpenbeck et al., Phys. Rev. Lett. 130, 186301 (2023)] with other ideas from the equilibrium multi-orbital inchworm algorithm [Eidelstein et al., Phys. Rev. Lett. 124, 206405 (2020)]. We verify our method by comparison with analytical limits and numerical results from previous methods.

Decomposing Imaginary-Time Feynman Diagrams Using Separable Basis Functions: Anderson Impurity Model Strong-Coupling Expansion

We present a deterministic algorithm for the efficient evaluation of imaginary-time diagrams based on the recently introduced discrete Lehmann representation (DLR) of imaginary-time Green’s functions. In addition to the efficient discretization of diagrammatic integrals afforded by its approximation properties, the DLR basis is separable in imaginary-time, allowing us to decompose diagrams into linear combinations of nested sequences of one-dimensional products and convolutions. Focusing on the strong-coupling bold-line expansion of generalized Anderson impurity models, we show that our strategy reduces the computational complexity of evaluating an Mth-order diagram at inverse temperature β and spectral width ωmax from O((βωmax)2M−1) for a direct quadrature to O(M(log(βωmax))M+1), with controllable high-order accuracy. We benchmark our algorithm using third-order expansions for multiband impurity problems with off-diagonal hybridization and spin-orbit coupling, presenting comparisons with exact diagonalization and quantum Monte Carlo approaches. In particular, we perform a self-consistent dynamical mean-field theory calculation for a three-band Hubbard model with strong spin-orbit coupling representing a minimal model of Ca2RuO4, demonstrating the promise of the method for modeling realistic strongly correlated multiband materials. For both strong and weak coupling expansions of low and intermediate order, in which diagrams can be enumerated, our method provides an efficient, straightforward, and robust blackbox evaluation procedure. In this sense, it fills a gap between diagrammatic approximations of the lowest order, which are simple and inexpensive but inaccurate, and those based on Monte Carlo sampling of high-order diagrams. Published by the American Physical Society 2024

Preparation, optical properties, room temperature ferromagnetism, and mechanism of ordered nanotube-like tantalum oxide films

Physical property changes caused by defects have recently attracted significant attention due to their potential applications in sensors, spintronic devices, and multifunctional memory. Due to their numerous surface defects, this study fabricated ordered Ta2O5 nanotube (NT) thin films on Ta foil through an anodization technique. Then, the oxygen bubble model was applied to explain the formation of NTs from the perspective of lattice orientation. Furthermore, this study investigated influence of anodization duration and annealing treatment on the crystal structure, optical properties, and magnetic behavior. Notably, room-temperature ferromagnetism was observed in the as-prepared Ta2O5 NTs for the first time. After annealing in an argon atmosphere, the band gap of the sample decreased, accompanied by an increase in ferromagnetism. The underlying mechanism for this phenomenon was elucidated using a hydrogen-like impurity model. Consequently, this study on the magnetism of Ta2O5 NTs holds excellent potential for expanding their application in spin electronic devices.

Many-Body Quantum Interference Route to the Two-Channel Kondo Effect: Inverse Design for Molecular Junctions and Quantum Dot Devices.

Molecular junctions-whether actual single molecules in nanowire break junctions or artificial molecules realized in coupled quantum dot devices-offer unique functionality due to their orbital complexity, strong electron interactions, gate control, and many-body effects from hybridization with the external electronic circuit. Inverse design involves finding candidate structures that perform a desired function optimally. Here we develop an inverse design strategy for generalized quantum impurity models describing molecular junctions, and as an example, use it to demonstrate that many-body quantum interference can be leveraged to realize the two-channel Kondo critical point in simple 4- or 5-site molecular moieties. We show that remarkably high Kondo temperatures can be achieved, meaning that entropy and transport signatures should be experimentally accessible.

Error mitigation in variational quantum eigensolvers using tailored probabilistic machine learning

Quantum computing technology has the potential to revolutionize the simulation of materials and molecules in the near future. A primary challenge in achieving near-term quantum advantage is effectively mitigating the noise effects inherent in current quantum processing units (QPUs). This challenge is also decisive in the context of quantum-classical hybrid schemes employing variational quantum eigensolvers (VQEs) that have attracted significant interest in recent years. In this paper, we present a method that employs parametric Gaussian process regression (GPR) within an active learning framework to mitigate noise in quantum computations, focusing on VQEs. Our approach, grounded in probabilistic machine learning, exploits a custom prior based on the VQE ansatz to capture the underlying correlations between VQE outputs for different variational parameters, thereby enhancing both accuracy and efficiency. We demonstrate the effectiveness of our method on a two-site Anderson impurity model and a eight-site Heisenberg model, using the IBM open-source quantum computing framework, Qiskit, showcasing substantial improvements in the accuracy of VQE outputs while reducing the number of direct QPU energy evaluations. This paper contributes to the ongoing efforts in quantum-error mitigation and optimization, bringing us a step closer to realizing the potential of quantum computing in quantum matter simulations. Published by the American Physical Society 2024

Downfolding from ab initio to interacting model Hamiltonians: comprehensive analysis and benchmarking of the DFT+cRPA approach

Model Hamiltonians are regularly derived from first principles to describe correlated matter. However, the standard methods for this contain a number of largely unexplored approximations. For a strongly correlated impurity model system, here we carefully compare a standard downfolding technique with the best possible ground-truth estimates for charge-neutral excited-state energies and wave functions using state-of-the-art first-principles many-body wave function approaches. To this end, we use the vanadocene molecule and analyze all downfolding aspects, including the Hamiltonian form, target basis, double-counting correction, and Coulomb interaction screening models. We find that the choice of target-space basis functions emerges as a key factor for the quality of the downfolded results, while orbital-dependent double-counting corrections diminish the quality. Background screening of the Coulomb interaction matrix elements primarily affects crystal-field excitations. Our benchmark uncovers the relative importance of each downfolding step and offers insights into the potential accuracy of minimal downfolded model Hamiltonians.

Hybridization of an s-wave impurity with graphene lattice

Hybridization function is a quantity characterizing electron hoppings between an impurity and a host material in which the impurity resides, a full understandinging of it is crucial for studying correlation effects in various impurity problems. This work studies the hybridization function for the Anderson impurity model describing a single-orbital impurity on a honeycomb lattice simulating graphene and presents a calculation approach to obtain this function at low energy. Within this approach, the general form of the hybridization function in graphene is presented and analytical expressions of low-energy hybridization spectrum are obtained. The results quantitatively match numerical solutions for different impurity positions on the lattice. The effect of the low-energy hybridization spectrum and the capability to predict the correlated effects of the impurity problem are discussed thoroughly, suggesting that different types of pseudogap Kondo effect may occur at different impurity positions.