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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Scalable semidefinite programming approach to variational embedding for quantum many-body problems

In quantum embedding theories, a quantum many-body system is divided into localized clusters of sites which are treated with an accurate ‘high-level’ theory and glued together self-consistently by a less accurate ‘low-level’ theory at the global scale. The recently introduced variational embedding approach for quantum many-body problems combines the insights of semidefinite relaxation and quantum embedding theory to provide a lower bound on the ground-state energy that improves as the cluster size is increased. The variational embedding method is formulated as a semidefinite program (SDP), which can suffer from poor computational scaling when treated with black-box solvers. Here, we exploit the interpretation of this SDP as an embedding method to develop an algorithm which alternates parallelizable local updates of the high-level quantities with updates that enforce the low-level global constraints. Moreover, we show how translation invariance in lattice systems can be exploited to reduce the complexity of projecting a key matrix to the positive semidefinite cone.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Intrinsic operators for the translationally-invariant many-body problem

Abstract The need to enforce fermionic antisymmetry in the nuclear many-body problem commonly requires use of single-particle coordinates, defined relative to some fixed origin. To obtain physical operators which nonetheless act on the nuclear many-body system in a Galilean-invariant fashion, thereby avoiding spurious center-of-mass contributions to observables, it is necessary to express these operators with respect to the translational intrinsic frame. Several commonly-encountered operators in nuclear many-body calculations, including the magnetic dipole and electric quadrupole operators (in the impulse approximation) and generators of U(3) and Sp ( 3 , R ) symmetry groups, are bilinear in the coordinates and momenta of the nucleons and, when expressed in intrinsic form, become two-body operators. To work with such operators in a second-quantized many-body calculation, it is necessary to relate three distinct forms: the defining intrinsic-frame expression, an explicitly two-body expression in terms of two-particle relative coordinates, and a decomposition into one-body and separable two-body parts. We establish the relations between these forms, for general (non-scalar and non-isoscalar) operators bilinear in coordinates and momenta.

Physics↗
DOE OSTI2022

Provably efficient machine learning for quantum many-body problems

Classical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry. However, the advantages of ML over traditional methods have not been firmly established. In this work, we prove that classical ML algorithms can efficiently predict ground-state properties of gapped Hamiltonians after learning from other Hamiltonians in the same quantum phase of matter. By contrast, under a widely accepted conjecture, classical algorithms that do not learn from data cannot achieve the same guarantee. We also prove that classical ML algorithms can efficiently classify a wide range of quantum phases. Extensive numerical experiments corroborate our theoretical results in a variety of scenarios, including Rydberg atom systems, two-dimensional random Heisenberg models, symmetry-protected topological phases, and topologically ordered phases.

Science & Technology - Other Topics↗
DOE OSTI2023

Transformer quantum state: A multipurpose model for quantum many-body problems

Here, inspired by the advancements in large language models based on transformers, we introduce the transformer quantum state (TQS): a versatile machine learning model for quantum many-body problems. In sharp contrast to Hamiltonian/task specific models, TQS can generate the entire phase diagram, predict field strengths with experimental measurements, and transfer such a knowledge to new systems it has never been trained on before, all within a single model. With specific tasks, fine-tuning the TQS produces accurate results with small computational cost. Versatile by design, TQS can be easily adapted to new tasks, thereby pointing towards a general-purpose model for various challenging quantum problems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Neural-network quantum states for the nuclear many-body problem

A long-standing goal of nuclear theory is to explain how the structure and dynamics of atomic nuclei and neutron-star matter emerge from the underlying interactions among protons and neutrons. Achieving this goal requires solving the nuclear quantum many-body problem with high accuracy across a wide range of length scales and density regimes. In this review, we discuss how artificial neural network representations of the nuclear many-body wave function have significantly extended the capabilities of continuum quantum Monte Carlo methods. In particular, neural network quantum states enable calculations of larger systems than were previously accessible and provide a flexible framework for capturing phenomena that challenge conventional approaches, including the emergence of nuclear clusters and superfluid phases in dense matter. We highlight recent applications to finite nuclei, infinite nuclear and neutron matter, and dynamical processes relevant to lepton-nucleus and nucleus-nucleus scattering. We also discuss conceptual and methodological connections with condensed matter physics, emphasizing developments in neural network quantum states that bridge strongly correlated systems across disciplines. Together, these developments demonstrate how neural-network methods open new avenues toward unified and accurate descriptions of nuclear structure, matter, and reactions.

Lovato, Alessandro [Argonne; TIFPA-INFN, Trento; V↗
DOE OSTI2024

Wavefunction matching for solving quantum many-body problems

Ab initio calculations have an essential role in our fundamental understanding of quantum many-body systems across many subfields, from strongly correlated fermions to quantum chemistry and from atomic and molecular systems to nuclear physics. One of the primary challenges is to perform accurate calculations for systems where the interactions may be complicated and difficult for the chosen computational method to handle. Here we address the problem by introducing an approach called wavefunction matching. Wavefunction matching transforms the interaction between particles so that the wavefunctions up to some finite range match that of an easily computable interaction. This allows for calculations of systems that would otherwise be impossible owing to problems such as Monte Carlo sign cancellations. We apply the method to lattice Monte Carlo simulations of light nuclei, medium-mass nuclei, neutron matter and nuclear matter. We use high-fidelity chiral effective field theory interactions and find good agreement with empirical data. These results are accompanied by insights on the nuclear interactions that may help to resolve long-standing challenges in accurately reproducing nuclear binding energies, charge radii and nuclear-matter saturation in ab initio calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Genetic programming for the nuclear many-body problem: a guide

Genetic Programming (GP) is an evolutionary algorithm that generates computer programs, or mathematical expressions, to solve complex problems. In this Guide, we demonstrate how to use GP to develop surrogate models to mitigate the computational costs of modeling atomic nuclei with ever increasing complexity. The computational burden escalates when uncertainty quantification is pursued, or when observables must be globally computed for thousands of nuclei. By studying three models in which the mean field depends on the total particle density self-consistently, we show that by constructing reduced order models supported by GP one can speed up many-body computations by several orders of magnitude with a negligible loss in accuracy.

dimensionality reduction↗
DOE OSTI2021

Dimensionality reduction of the many-body problem using coupled-cluster subsystem flow equations: classical and quantum computing perspective

We discuss reduced-scaling strategies employing recently introduced sub-system embedding sub-algebras coupled-cluster formalism (SES-CC) to describe many-body systems. These strategies utilize properties of the SES-CC formulations where the equations describing certain classes of sub- systems can be integrated into a computational flows composed coupled eigenvalue problems of reduced dimensionality. Additionally, these flows can be defined at the level of the CC Ansatz defined by selected classes of cluster amplitudes, which define the wave function ”memory” of possible partitionings of the many-body system into constituent sub-systems. One of the possible ways of solving these coupled problems is through implementing procedures, where the information is passed between the sub-systems in a self-consistent manner. As a special case, we consider local flow formulations where the so-called local character of correlation effects can be closely related to properties of sub-system embedding sub-algebras employing localized molecular basis. We also generalize flow equations to the time domain and to downfolding methods utilizing double exponential unitary CC Ansatz (DUCC), where reduced dimensionality of constituent sub-problems offer a possibility of efficient utilization of limited quantum resources in modeling realistic systems.

Electron correlation, quantum chemistry, quantum c↗
DOE OSTI2020

Finite temperature auxiliary field quantum Monte Carlo in the canonical ensemble

Finite temperature auxiliary field-based quantum Monte Carlo methods, including determinant quantum Monte Carlo and Auxiliary Field Quantum Monte Carlo (AFQMC), have historically assumed pivotal roles in the investigation of the finite temperature phase diagrams of a wide variety of multidimensional lattice models and materials. Despite their utility, however, these techniques are typically formulated in the grand canonical ensemble, which makes them difficult to apply to condensates such as superfluids and difficult to benchmark against alternative methods that are formulated in the canonical ensemble. Working in the grand canonical ensemble is furthermore accompanied by the increased overhead associated with having to determine the chemical potentials that produce desired fillings. Given this backdrop, in this work, we present a new recursive approach for performing AFQMC simulations in the canonical ensemble that does not require knowledge of chemical potentials. To derive this approach, we exploit the convenient fact that AFQMC solves the many-body problem by decoupling many-body propagators into integrals over one-body problems to which non-interacting theories can be applied. We benchmark the accuracy of our technique on illustrative Bose and Fermi–Hubbard models and demonstrate that it can converge more quickly to the ground state than grand canonical AFQMC simulations. We believe that our novel use of HS-transformed operators to implement algorithms originally derived for non-interacting systems will motivate the development of a variety of other methods and anticipate that our technique will enable direct performance comparisons against other many-body approaches formulated in the canonical ensemble.

Shen, Tong (ORCID:0000000206292468)↗
DOE OSTI2020

Complex Langevin and other approaches to the sign problem in quantum many-body physics

In this work, we review the theory and applications of complex stochastic quantization to the quantum many-body problem. Along the way, we present a brief overview of a number of ideas that either ameliorate or in some cases altogether solve the sign problem, including the classic reweighting method, alternative Hubbard–Stratonovich transformations, dual variables (for bosons and fermions), Majorana fermions, density-of-states methods, imaginary asymmetry approaches, and Lefschetz thimbles. We discuss some aspects of the mathematical underpinnings of conventional stochastic quantization, provide a few pedagogical examples, and summarize open challenges and practical solutions for the complex case. Finally, we review the recent applications of complex Langevin to quantum field theory in relativistic and nonrelativistic quantum matter, with an emphasis on the nonrelativistic case.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Dipolar molecule emulator of lattice gauge theories (Final Report)

The quantum many-body problem is a great unsolved, cross-cutting challenge in physics that is of fundamental importance. Our understanding of phenomena related to dense quark matter, in particular, is challenged by this practical intractability of classical simulations. Because of the sheer cost and challenge of performing experiments that probe the length and energy scales relevant to such physics, there are practical motivations for finding theoretical methods to address the many-body problem. One promising approach is based on the use of a programmable and controllable analog quantum systems to emulate the physics of many-body problems of interest. While there are currently broad efforts to develop mid- to large-scale quantum computers, we are still likely many years away from such devices outperforming classical supercomputers for useful calculations. Even though digital quantum computers are still at a stage too premature for such tasks, approaches based on analog quantum simulators have advanced rapidly over the past two decades and can now treat many-body problems of interest on small- to medium-scale systems. Tackling the challenging many-body problems of relevance to high energy physics represents one of the great new opportunities and challenges for the field of analog quantum simulation. To address this challenge, this award brought together an interdisciplinary team of physicists with expertise in high energy theory (El-Khadra and Draper), computational and condensed matter physics (Clark), and experimental quantum and atomic, molecular, optical (AMO) science (DeMarco and Gadway), with the goal of developing realistic and optimized strategies for the analog quantum simulation of lattice gauge theories using cold atoms and molecules. This track 1 project included both theoretical and experimental goals, stated as follows. The theory goals were to "develop and verify a novel approach to quantum emulation of (1+1)d quantum link models, based on arrays of trapped quantum spins with long-range interactions." This final project report details the progress made under this award, as well as new research directions developed under this award.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Transferability of data-driven, many-body models for CO 2 simulations in the vapor and liquid phases

Here, extending on the previous work by Riera et al. [J. Chem. Theory Comput. 16, 2246–2257 (2020)], we introduce a second generation family of data-driven many-body MB-nrg models for CO 2 and systematically assess how the strength and anisotropy of the CO 2 –CO 2 interactions affect the models’ ability to predict vapor, liquid, and vapor–liquid equilibrium properties. Building upon the many-body expansion formalism, we construct a series of MB-nrg models by fitting one-body and two-body reference energies calculated at the coupled cluster level of theory for large monomer and dimer training sets. Advancing from the first generation models, we employ the charge model 5 scheme to determine the atomic charges and systematically scale the two-body energies to obtain more accurate descriptions of vapor, liquid, and vapor–liquid equilibrium properties. Challenges in model construction arise due to the anisotropic nature and small magnitude of the interaction energies in CO 2 , calling for the necessity of highly accurate descriptions of the multidimensional energy landscape of liquid CO 2 . These findings emphasize the key role played by the training set quality in the development of transferable, data-driven models, which, accurately representing high-dimensional many-body effects, can enable predictive computer simulations of molecular fluids across the entire phase diagram.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Hydrogen bond arrangements in (H 2 O) 20, 24, 28 clathrate hydrate cages: Optimization and many-body analysis

Here we provide a detailed study of hydrogen bonding arrangements, relative stability, residual entropy, and an analysis of the many-body effects in the (H 2 O) 20 (D-cage), (H 2 O) 24 (T-cage), and (H 2 O) 28 (H-cage) hollow cages making up structures I (sI) and II (sII) of clathrate hydrate lattices. Based on the enumeration of the possible hydrogen bonding networks for a fixed oxygen atom scaffold, the residual entropy (S 0 ) of these three gas phase cages was estimated at 0.754 82, 0.754 44, and 0.754 17 · Nk b , where N is the number of molecules and k b is Boltzmann’s constant. A previously identified descriptor of enhanced stability based on the relative arrangement and connectivity of nearest-neighbor fragments on the polyhedral water cluster [strong-weak-effective-bond model] also applies to the larger hollow cages. The three cages contain a maximum of 7, 9, and 11 such preferable arrangements of trans nearest dimer pairs with one “free” OH bond on the donor molecule (t1d dimers). The Many-Body Expansion (MBE) up to the 4-body suggests that the many-body terms vary nearly linearly with the cluster binding energy. Using a hierarchical approach of screening the relative stability of networks starting from optimizations with the TIP4P, TTM2.1-F, and MB-pol classical potentials, subsequently refining at more accurate levels of electronic structure theory (DFT and MP2), and finally correcting for zero-point energy, we were able to identify a group of four low-lying isomers of the (H 2 O) 24 T-cage, two of which are antisymmetric and the other two form a pair of antipode configurations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

GFCCLib: Scalable and efficient coupled-cluster Green's function library for accurately tackling many-body electronic structure problems

Coupled-cluster Green’s function (GFCC) calculation has drawn much attention in the recent years for targeting the molecular and material electronic structure problems from a many-body perspective in a systematically improvable way. However, GFCC calculations on scientific computing clusters usually suffer from expensive higher di- mensional tensor contractions in the complex space, expensive inter-process communi- cation, and severe load imbalance, which limits it’s routine use for tackling electronic structure problems. Here we present a numerical library prototype that is specifically designed for large-scale GFCC calculations. The design of the library is focused on a systematically optimal computing strategy to improve its scalability and efficiency. The performance of the library is demonstrated by the relevant profiling analysis of running GFCC calculations on remote giant computing clusters. The capability of the library is highlighted by computing a wide near valence band of a fullerene C60 molecule for the first time at the GFCCSD level that shows excellent agreement with the experimental spectrum.

Peng, Bo↗
DOE OSTI2025

Predicting nonequilibrium Green’s function dynamics and photoemission spectra via nonlinear integral operator learning

Understanding the dynamics of nonequilibrium quantum many-body systems is an important research topic in a wide range of fields across condensed matter physics, quantum optics, and high-energy physics. However, numerical studies of large-scale nonequilibrium phenomena in realistic materials face serious challenges due to intrinsic high-dimensionality of quantum many-body problems and the absence of time-invariance. The nonequilibrium properties of many-body systems can be described by the dynamics of the correlator, or the Green's function of the system, whose time evolution is given by a high-dimensional system of integro-differential equations, known as the Kadanoff–Baym equations (KBEs). The time-convolution term in KBEs, which needs to be recalculated at each time step, makes it difficult to perform long-time numerical simulation. In this paper, we develop an operator-learning framework based on recurrent neural networks (RNNs) to address this challenge. We utilize RNNs to learn the nonlinear mapping between Green's functions and convolution integrals in KBEs. By using the learned operators as a surrogate model in the KBE solver, we obtain a general machine-learning scheme for predicting the dynamics of nonequilibrium Green's functions. Besides significant savings per each time step, the new methodology reduces the temporal computational complexity from $O(N_t^3)$ to $O(N_t)$ where N t is the number of steps taken in a simulation, thereby making it possible to study large many-body problems which are currently infeasible with conventional KBE solvers. Through various numerical examples, we demonstrate the effectiveness of the operator-learning based approach in providing accurate predictions of physical observables such as the reduced density matrix and time-resolved photoemission spectra. Moreover, our framework exhibits clear numerical convergence and can be easily parallelized, thereby facilitating many possible further developments and applications.

97 MATHEMATICS AND COMPUTING↗