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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Application of the locally self-consistent embedding approach to the Anderson model with non-uniform random distributions

Highlights: • Typical Medium Theory (TMT) for the Anderson Localization. • Locally Self-Consistent Multiple Scattering Method (LSMS) for Random Disordered Systems. • Linear Scaling Computational Method for Random Disordered Systems. We apply the recently developed embedding scheme for the locally self-consistent method to random disorder electrons systems. The method is based on the locally self-consistent multiple scattering theory and the typical medium theory. The locally self-consistent multiple scattering theory divides a system into many small designated local interaction zones. The subsystem within each local interaction zone is embedded in a self-consistent field from the typical medium theory. This approximation allows the study of random systems with large numbers of sites. We present results for the three dimensional Anderson model with different random disorder potential distributions. Using the typical density of states as an indicator of Anderson localization, we find that the method can capture the localization for commonly studied disorder potentials. These include the uniform distribution, the Gaussian distribution, and even the unbounded Cauchy distribution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Spectral properties of three-dimensional Anderson model

The three-dimensional Anderson model represents a paradigmatic model to understand the Anderson localization transition. In this work we first review some key results obtained for this model in the past 50 years, and then study its properties from the perspective of modern numerical approaches. Our main focus is on the quantitative comparison between the level sensitivity statistics and the level statistics. While the former studies the sensitivity of Hamiltonian eigenlevels upon inserting a magnetic flux, the latter studies the properties of unperturbed eigenlevels. We define two versions of dimensionless conductance, the first corresponding to the width of the level curvature distribution relative to the mean level spacing, and the second corresponding to the ratio of the Heisenberg time and the Thouless time obtained from the spectral form factor. We show that both conductances look remarkably similar around the localization transition, in particular, they predict a nearly identical critical point consistent with other well-established measures of the transition. We then study some further properties of those quantities: for level curvatures, we discuss particular similarities and differences between the width of the level curvature distribution and the characteristic energy studied by Edwards and Thouless (1972) in their pioneering work, in which the hopping at one lattice edge is changed from periodic to antiperiodic boundary conditions. In the context of the spectral form factor, we show that at the critical point it enters a broad time-independent regime, in which its value is consistent with the level compressibility obtained from the level variance. Finally, we test the scaling solution of the average level spacing ratio in the crossover regime using the cost function minimization approach introduced recently in Šuntajs et al. (2020). The latter approach seeks for the optimal scaling solution in the vicinity of the crossing point, while at the same time it allows for the crossing point to drift due to finite-size corrections. We find that the extracted transition point and the scaling coefficient agree with those from the literature to high numerical accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Magnetic and singlet phases in the three-dimensional periodic Anderson Model

Heavy-fermion materials are compounds in which localized f orbitals hybridize with delocalized d ones, leading to quasiparticles with large renormalized masses. The presence of strongly correlated f electrons at the Fermi level may also lead to long-range order, such as magnetism, or unconventional superconductivity. From a theoretical point of view, the “standard model” for heavy-fermion compounds is the periodic Anderson model (PAM). Despite being extensively scrutinized, its thermodynamic properties in three-dimensional (3D) lattices have not been carefully addressed by unbiased methodologies. Here we investigate the 3D PAM employing state-of-the-art finite-temperature auxiliary-field quantum Monte Carlo simulations. Furthermore, we present the behavior of the kinetic energy, the entropy, the specific heat, and the double occupancy as functions of the temperature and the hybridization strength. From these quantities, and by the analysis of the spin-spin correlation functions, we investigate the occurrence of magnetic phase transitions at finite temperatures, and we determine the phase diagram of the model, including the behavior of the Néel temperature as a function of the external parameters.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1987

Ground-state properties of the periodic Anderson model

The ground-state energy, hybridization matrix element, local moment, and spin-density correlations of a one-dimensional, finite-chain, periodic, symmetric Anderson model are obtained by numerical simulations and compared with perturbation theory and strong-coupling results. It is found that the local f-electron spins are compensated by correlation with other f-electrons as well as band electrons leading to a nonmagnetic ground state.

Blankenbecler, R.↗
DOE OSTI2026

Quantum solver for single-impurity Anderson models with particle-hole symmetry

Quantum embedding methods, such as dynamical mean-field theory (DMFT), provide a powerful framework for investigating strongly correlated materials. A central computational bottleneck in DMFT is in solving the Anderson impurity model (AIM), whose exact solution is classically intractable for large bath sizes. In this work, we benchmark a quantum-classical hybrid solver tailored for particle-hole symmetric AIMs, using the variational quantum eigensolver to prepare the ground state of the model with shallow quantum circuits. The solver uses shallow quantum ansätze and one set of variational parameters to prepare the ground state and its particle and hole excitations, enabling the construction of the impurity Green’s function through a continued-fraction expansion. We evaluate the performance of this approach across a few bath sizes and interaction strengths under noisy, shot-limited conditions. We compare three optimization routines (COBYLA, Adam, and L-BFGS-B) in terms of convergence and fidelity, assess the benefits of estimating a quantum-computed moment correction to the variational energies, and benchmark the approach by comparing the density of states computed from the impurity Green’s function against that obtained using a classical pipeline. Our results demonstrate the feasibility of Green’s function construction on near-term devices and establish practical benchmarks for quantum impurity solvers embedded within self-consistent DMFT loops.

Karabin, Mariia [ORNL]↗
DOE OSTI2023

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 nonequilibrium 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.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Anderson Acceleration for Distributed Training of Deep Learning Models

Anderson acceleration (AA) is an extrapolation technique that has recently gained interest in the deep learning (DL) community to speed-up the sequential training of DL models. However, when performed at large scale, the DL training is exposed to a higher risk of getting trapped into steep local minima of the training loss function, and standard AA does not provide sufficient acceleration to escape from these steep local minima. This results in poor generalizability and makes AA ineffective. To restore AA’s advantage to speed-up the training of DL models on large scale computing platforms, we combine AA with an adaptive moving average procedure that boosts the training to escape from steep local minima. By monitoring the relative standard deviation between consecutive iterations, we also introduce a criterion to automatically assess whether the moving average is needed. We applied the method to the following DL instantiations for image classification: (i) ResNet50 trained on the open-source CIFAR100 dataset and (ii) ResNet50 trained on the open-source ImageNet1k dataset. Numerical results obtained using up to 1,536 NVIDIA V100 GPUs on the OLCF supercomputer Summit showed the stabilizing effect of the moving average on AA for all the problems above.

Lupo Pasini, Massimiliano↗
DOE OSTI2025

Dynamic, symmetry-preserving, and hardware-adaptable circuits for quantum computing many-body states and correlators of the Anderson impurity model

We present a hardware-reconfigurable ansatz on N q -qubits for the variational preparation of many-body states of the Anderson impurity model (AIM) with N imp + N bath = N q /2 sites, which conserves total charge and spin z component within each variational search subspace. The many-body ground state of the AIM is determined as the minimum over all minima of O(N$^2_ q$) distinct charge-spin sectors. Hamiltonian expectation values are shown to require ω(N q ) < N meas. $\leqslant$ O(N imp N bath ) symmetry-preserving, parallelizable measurement circuits, each amenable to postselection. To obtain the one-particle impurity Green’s function we show how initial Krylov vectors can be computed via midcircuit measurement and how Lanczos iterations can be computed using the symmetry-preserving ansatz. For a single-impurity Anderson model with a number of bath sites increasing from one to seven, we show using numerical emulation that the ease of variational ground-state preparation is suggestive of linear scaling in circuit depth and subquartic scaling in optimizer complexity. We therefore expect that, combined with time-dependent methods for Green’s function computation, our ansatz provides a useful tool to account for electronic correlations on early fault-tolerant processors. Finally, with a view towards computing real materials properties of interest like magnetic susceptibilities and electron-hole propagators, we provide a straightforward method to compute many-body, time-dependent correlation functions using a combination of time evolution, midcircuit measurement-conditioned operations, and the Hadamard test.

36 MATERIALS SCIENCE↗
NASA NTRS1989

IR emission and UV extinction in two open clusters

Recent models of interstellar extinction have shown the importance of understanding both the UV and IR properties of interstellar dust grains. IRAS data have shown variations in 60 and 100 micron emissions presumably due to the presence of IR cirrus, while recent observations in the UV by Fitzpatrick and Massa have identified components in the UV extinction curve which vary in different star regions. A Draine and Anderson model connects these results by proposing that different size variations in interstellar grains would cause distinct changes in both the IR emission and the UV extinction. In order to test this model it is necessary to make observations in well defined locations away from peculiar extinction regions. In the infrared this means looking away from the galactic plane so as to limit non-local sources of IR radiation. Two open clusters that are out of the galactic plane and which contain a number of late B and early A stars suitable for UV extinction studies, and whose IRAS data show variations in the 60/100 micron ratio were studied. Based on the Drain and Anderson model, variations were expected in their UV extinction curves that correlate with the IR cirrus emission.

Hackwell, James A.↗
NASA NTRS1982

Possible contributions of supernova remnants to the soft X-ray diffuse background (0.1 - 1keV)

Almost all of the B band (0.10-0.19 keV) and C band (0.15-0.28 keV) X-rays probably originate in a hot region surrounding the Sun, which Cox and Anderson modeled as a supernova remnant. This same region may account for a significant fraction of the M band (0.5-1 keV) X-rays if the nonequilibrium models of Cox and Anderson are applicable. A population of distant SNR similar to the local region, with center-to-center spacing of about 300 pc, could provide enough galactic M band emission to fill in the dip in the count rate in the galactic plane that would otherwise be present due to absorption of both the extra galactic power law flux and any large-scale-height stellar (or galactic halo) emission.

Sanders, W. T.↗
NASA NTRS1983

Possible contributions of supernova remnants to the soft X-ray diffuse background (0.1 - 1 keV)

Almost all of the B band (0. 10-0.19 keV) and C band (0.15-0.28 keV) X-rays probably originate in a hot region surrounding the sun, which Cox and Anderson modeled as a supernova remnant. This same region may account for a significant fraction of the M band (0.5-1 keV) X-rays if the nonequilibrium models of Cox and Anderson are applicable. A population of distant SNR similar to the local region, with center-to-center spacing of about 300 pc, could provide enough galactic M band emission to fill in the dip in the count rate in the galactic plane that would otherwise be present due to absorption of both the extra galactic power law flux and any large-scale-height stellar (or galactic halo) emission.

Sanders, W. T.↗
DOE OSTI2024

Interaction Effects on the Dynamical Anderson Metal-Insulator Transition Using Kicked Quantum Gases

Understanding the interplay of interaction and disorder in quantum transport poses long-standing scientific challenges for theory and experiment. While highly controlled ultracold atomic platforms combining atomic interactions with spatially disordered lattices have led to remarkable advances, the extension of such controlled studies to phenomena in high-dimensional disordered systems, such as the three-dimensional Anderson metal-insulator transition has been limited. Kicked quantum gases provide an alternate experimental platform that captures the Anderson model in momentum space and features dynamical localization as the analog of Anderson localization. Here, we utilize a momentum space lattice platform using quasiperiodically kicked ultracold atomic gases to experimentally investigate interaction effects on the three-dimensional dynamical Anderson metal-insulator transition. Here, we observe interaction-driven subdiffusion and a divergence of delocalization onset time on approaching the phase boundary. Mean-field numerical simulations show qualitative agreement with experimental observations, but with significant quantitative deviations.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Tensor train continuous time solver for quantum impurity models

The simulation of strongly correlated quantum impurity models is a significant challenge in modern condensed matter physics that has multiple important applications. Thus far, the most successful methods for approaching this challenge involve Monte Carlo techniques that accurately and reliably sample perturbative expansions to any order. However, the cost of obtaining high precision through these methods is high. Recently, tensor train decomposition techniques have been developed as an alternative to Monte Carlo integration. In this study, we apply these techniques to the single-impurity Anderson model at equilibrium by calculating the systematic expansion in power of the hybridization of the impurity with the bath. Furthermore, we demonstrate the performance of the method in a paradigmatic application, examining the first-order phase transition on the infinite-dimensional Bethe lattice, which can be mapped to an impurity model through dynamical mean field theory. Our results indicate that using tensor train decomposition schemes allows the calculation of finite-temperature Green's functions and thermodynamic observables with unprecedented accuracy. The methodology holds promise for future applications to frustrated multiorbital systems, using a combination of partially summed series with other techniques pioneered in diagrammatic and continuous time quantum Monte Carlo.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Spatially dispersing Yu-Shiba-Rusinov states in the unconventional superconductor FeTe 0.55 Se 0.45

By using scanning tunneling microscopy (STM) we find and characterize dispersive, energy-symmetric in-gap states in the iron-based superconductor FeTe 0.55 Se 0.45 , a material that exhibits signatures of topological superconductivity, and Majorana bound states at vortex cores or at impurity locations. We use a superconducting STM tip for enhanced energy resolution, which enables us to show that impurity states can be tuned through the Fermi level with varying tip-sample distance. We find that the impurity state is of the Yu-Shiba-Rusinov (YSR) type, and argue that the energy shift is caused by the low superfluid density in FeTe 0.55 Se 0.45 , which allows the electric field of the tip to slightly penetrate the sample. We model the newly introduced tip-gating scenario within the single-impurity Anderson model and find good agreement to the experimental data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗