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Gull, Emanuel

Publications and source records attributed to Gull, Emanuel.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Quantum-centric supercomputing for materials science: A perspective on challenges and future directions

Computational models are an essential tool for the design, characterization, and discovery of novel materials. Computationally hard tasks in materials science stretch the limits of existing high-performance supercomputing centers, consuming much of their resources for simulation, analysis, and data processing. Quantum computing, on the other hand, is an emerging technology with the potential to accelerate many of the computational tasks needed for materials science. In order to do that, the quantum technology must interact with conventional high-performance computing in several ways: approximate results validation, identification of hard problems, and synergies in quantum-centric supercomputing. Here in this paper, we provide a perspective on how quantum-centric supercomputing can help address critical computational problems in materials science, the challenges to face in order to solve representative use cases, and new suggested directions.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Denoising and Extension of Response Functions in the Time Domain

Response functions of quantum systems, such as electron Green’s functions, magnetic, or charge susceptibilities, describe the response of a system to an external perturbation. They are the central objects of interest in field theories and quantum computing and measured directly in experiment. Further, response functions are intrinsically causal. In equilibrium and steady-state systems, they correspond to a positive spectral function in the frequency domain. Since response functions define an inner product on a Hilbert space and thereby induce a positive definite function, the properties of this function can be used to reduce noise in measured data and, in equilibrium and steady state, to construct positive definite extensions for data known on finite time intervals, which are then guaranteed to correspond to positive spectra.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Robust analytic continuation of Green's functions via projection, pole estimation, and semidefinite relaxation

Green's functions of fermions are described by matrix-valued Herglotz-Nevanlinna functions. Since analytic continuation is fundamentally an ill-posed problem, the causal space described by the matrix-valued Herglotz-Nevanlinna structure can be instrumental in improving the accuracy and in enhancing the robustness with respect to noise. We demonstrate a three-pronged procedure for robust analytic continuation called PES: (1) projection of data to the causal space; (2) estimation of pole locations; and (3) semidefinite relaxation within the causal space. We compare the performance of PES with the recently developed Nevanlinna and Carathéodory continuation methods and find that PES is more robust in the presence of noise and does not require the usage of extended precision arithmetics. We also demonstrate that a causal projection improves the performance of the Nevanlinna and Carathéodory methods. The PES method is generalized to bosonic response functions, for which the Nevanlinna and Carathéodory continuation methods have not yet been developed. Furthermore, it is particularly useful for studying spectra with sharp features, as they occur in the study of molecules and band structures in solids.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Fully self-consistent finite-temperature $GW$ in Gaussian Bloch orbitals for solids

In this work, we present algorithmic and implementation details for the fully self-consistent finite-temperature $GW$ method in Gaussian Bloch orbitals for solids. Our implementation is based on the finite-temperature Green's function formalism in which all equations are solved on the imaginary axis, without resorting to analytical continuation during the self-consistency. No quasiparticle approximation is employed and all matrix elements of the self-energy are explicitly evaluated. The method is tested by evaluating the band gaps of selected semiconductors and insulators. We show agreement with other, differently formulated, finite-temperature sc ⁢$GW$ implementations when finite-size corrections and basis-set errors are taken into account. By migrating computationally intensive calculations to graphics processing units, we obtain scalable results on large supercomputers with nearly optimal performance. Our work demonstrates the applicability of Gaussian orbital based sc⁢ $GW$ for ab initio correlated material simulations and provides a sound starting point for embedding methods built on top of $GW$.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Single- and two-particle finite size effects in interacting lattice systems

Simulations of extended quantum systems are typically performed by extrapolating results of a sequence of finite-system-size simulations to the thermodynamic limit. In the quantum Monte Carlo community, twist-averaging was pioneered as an efficient strategy to eliminate one-body finite size effects. In the dynamical mean field community, cluster generalizations of the dynamical mean field theory were formulated to study systems with nonlocal correlations. In this work, we put the twist-averaging and the dynamical cluster approximation variant of the dynamical mean field theory onto equal footing, discuss commonalities and differences, and compare results from both techniques to the standard periodic boundary technique. At the example of Hubbard-type models with local, short-range and Yukawa-like longer range interactions we show that all methods converge to the same limit, but that the convergence speed differs in practice. We show that embedding theories are an effective tool for managing both one-body and two-body finite size effects, in particular if interactions are averaged over twist angles.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Reduced Dynamics of Full Counting Statistics

We present a theory of modified reduced dynamics in the presence of counting fields. Reduced dynamics techniques are useful for describing open quantum systems at long emergent timescales when the memory timescales are short. However, they can be difficult to formulate for observables spanning the system and its environment, such as those characterizing transport properties. A large variety of mixed system--environment observables, as well as their statistical properties, can be evaluated by considering counting fields. Given a numerical method able to simulate the field-modified dynamics over the memory timescale, we show that the long-lived full counting statistics can be efficiently obtained from the reduced dynamics. We demonstrate the utility of the technique by computing the long-time current in the nonequilibrium Anderson impurity model from short-time Monte Carlo simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Relativistic self-consistent G W : Exact two-component formalism with one-electron approximation for solids

We present a formulation of relativistic self-consistent GW for solids based on the exact two-component formalism with one-electron approximation (X2C1e) and nonrelativistic Coulomb interactions. Our theory allows us to study scalar relativistic effects, spin-orbit coupling, and the interplay of relativistic effects with electron correlation without adjustable parameters. Our all-electron implementation is fully ab initio and does not require a pseudopotential constructed from atomic calculations. We examine the effect of the X2C1e approximation by comparison to the established four-component formalism and reach an excellent agreement. The simplicity of X2C1e enables the construction of higher order theories, such as embedding theories, on top of perturbative calculations.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Mechanism of superconductivity in the Hubbard model at intermediate interaction strength

We study the fluctuations responsible for pairing in the d -wave superconducting state of the two-dimensional Hubbard model at intermediate coupling within a cluster dynamical mean-field theory with a numerically exact quantum impurity solver. By analyzing how momentum- and frequency-dependent fluctuations generate the d -wave superconducting state in different representations, we identify antiferromagnetic fluctuations as the pairing glue of superconductivity in both the underdoped and the overdoped regime. Nevertheless, in the intermediate coupling regime, the predominant magnetic fluctuations may differ significantly from those described by conventional spin fluctuation theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Interaction-expansion inchworm Monte Carlo solver for lattice and impurity models

Multiorbital quantum impurity models with general interaction and hybridization terms appear in a wide range of applications, including embedding, quantum transport, and nanoscience. However, most quantum impurity solvers are restricted to a few impurity orbitals, discretized baths, diagonal hybridizations, or density-density interactions. We generalize the inchworm quantum Monte Carlo method to the interaction expansion, and we explore its application to typical single- and multiorbital problems encountered in investigations of impurity and lattice models. Our implementation generically outperforms bare and bold-line quantum Monte Carlo algorithms in the interaction expansion. For the systems studied here, our implementation remains inferior to the more specialized hybridization expansion and auxiliary field algorithms. So, the problem of convergence to unphysical fixed points, which hampers so-called bold-line methods, is not encountered in inchworm Monte Carlo.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Analytical continuation of matrix-valued functions: Carathéodory formalism

Finite-temperature quantum field theories are formulated in terms of Green's functions and self-energies on the Matsubara axis. In multiorbital systems, these quantities are related to positive semidefinite matrix-valued functions of the Carathéodory and Schur class. Analysis, interpretation, and evaluation of derived quantities such as real-frequency response functions requires analytic continuation of the off-diagonal elements to the real axis. Here we derive the criteria under which such functions exist for given Matsubara data and present an interpolation algorithm that intrinsically respects their mathematical properties. For small systems with precise Matsubara data, we find that the continuation exactly recovers all off-diagonal and diagonal elements. In real-materials systems, we show that the precision of the continuation is sufficient for the analytic continuation to commute with the Dyson equation, and we show that the truncation of the off-diagonal self-energy elements leads to considerable approximation artifacts.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Dynamical cluster approximation study of electron localization in the extended Hubbard model

We perform a detailed study of the phase transitions and mechanisms of electron localization in the extended Hubbard model using the dynamical cluster approximation on a 2×2 cluster. We explore the interplay of charge order and Mott physics. We find that a nearest-neighbor Coulomb interaction V causes “screening” effects close to the Mott phase transition, pushing the phase boundary to larger values of U. We also demonstrate the different effects of V on correlations in metallic and insulating regimes, and document the different correlation aspects of charge order and Mott states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Electron correlations in the cubic paramagnetic perovskite Sr ( V , Mn ) O 3 : Results from fully self-consistent self-energy embedding calculations

In this study, we use the thermodynamically consistent and conserving self-energy embedding theory (SEET) to study the spectra of the prototypical undistorted cubic perovskites SrVO 3 and SrMnO 3 . In the strongly correlated metallic SrVO 3 we find that the usual attribution of the satellite peaks at –1.8 eV to Hund or Hubbard physics in the t 2 g orbitals is inconsistent with our calculations. In the strongly correlated insulator SrMnO 3 we recover insulating behavior due to a feedback effect between the strongly correlated orbitals and the weakly correlated environment. Our calculation shows a systematic convergence of spectral features as the space of strongly correlated orbitals is enlarged, paving the way to a systematic parameter-free study of correlated perovskites.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Dynamic control of nonequilibrium metal-insulator transitions

Here, we demonstrate a first order metal-insulator phase transition in the repulsive, fully frustrated, single-band Hubbard model as a function of the coupling to a fermion bath. Time dependent manipulation of the bath coupling allows switching between metallic and insulating states both across the phase transition and within the coexistence region. We propose a simple nanoelectronic device for experimentally realizing dynamic control of the bath coupling. Analysis of the device characteristics shows that it can act as a two-terminal memristor.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Ab initio self-energy embedding for the photoemission spectra of NiO and MnO

The accurate ab initio simulation of periodic solids with strong correlations is one of the grand challenges of condensed matter. While mature methods exist for weakly correlated solids, the ab initio description of strongly correlated systems is an active field of research. In this work, we show results for the single-particle spectral function of the two correlated $\textit{d}$-electron solids NiO and MnO from self-energy embedding theory. Unlike earlier work, the theory does not use any adjustable parameters and is fully ab initio, while being able to treat both the strong correlation and the nonlocal screening physics of these materials. Here, we derive the method, discuss aspects of the embedding and choices of physically important orbitals, and compare our results to x-ray and angle-resolved photoemission spectroscopy as well as bremsstrahlung-isochromat spectroscopy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Multiorbital Quantum Impurity Solver for General Interactions and Hybridizations

Here we present a numerically exact inchworm Monte Carlo method for equilibrium multiorbital quantum impurity problems with general interactions and hybridizations. We show that the method, originally developed to overcome the dynamical sign problem in certain real-time propagation problems, can also overcome the sign problem as a function of temperature for equilibrium quantum impurity models. This is shown in several cases where the current method of choice, the continuous-time hybridization expansion, fails due to the sign problem. Our method therefore enables simulations of impurity problems as they appear in embedding theories without further approximations, such as the truncation of the hybridization or interaction structure or a discretization of the impurity bath with a set of discrete energy levels, and eliminates a crucial bottleneck in the simulation of ab initio embedding problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗