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Results for “Effective Hamiltonian models”

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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Statistical analysis for the neutrinoless double-β-decay matrix element of 48 Ca

Neutrinoless double-β-decay (0⁢vββ) nuclear matrix elements (NME) are the object of many theoretical calculation methods, and are very important for analysis and guidance of a large number of experimental efforts. However, there are large discrepancies between the NME values provided by different methods. Here, in this paper, we propose a statistical analysis of the 48 Ca 0v⁢ββ NME using the interacting shell model, emphasizing the range of the NME probable values and their correlations with observables that can be obtained from the existing nuclear data. Based on this statistical analysis with three independent effective Hamiltonians, we propose a common probability distribution function for the 0⁢vββ NME, which has a range of (0.45–0.95) at 90% confidence level, and a mean value of 0.68.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Two-atom-thin topological crystalline insulators lacking out of plane inversion symmetry

A two-dimensional topological crystalline insulator (TCI) with a single unit cell (u.c.) thickness is demonstrated here. To that end, one first shows that tetragonal (C 4 in-plane) symmetry is not a necessary condition for the creation of zero-energy metallic surface states on TCI slabs of finite-thicknesses, because zero-energy states persist even as all the in-plane rotational symmetries—furnishing topological protection—are completely removed. In other words, zero-energy levels on the model are not due to (nor are they protected by) topology. Furthermore, effective two-fold energy degeneracies taking place at few discrete k-points away from zero energy in the bulk Hamiltonian—that are topologically protected—persist at the u.c. thickness limit. Here, the chiral nature of the bulk TCI Hamiltonian permits creating a $2\times 2$ square Hamiltonian, whose topological properties remarkably hold invariant at both the bulk and at the single u.c. thickness limits. The identical topological characterization for bulk and u.c.-thick phases is further guaranteed by a calculation involving Pfaffians. This way, a two-atom-thick TCI is deployed hereby, in a demonstration of a topological phase that holds both in the bulk, and in two dimensions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Seniority eigenstate configuration interaction

Zero-seniority methods have shown great promise for the description of strongly correlated electronic systems. Other seniority sectors have been much less explored, and in particular, the maximal seniority sector and zero seniority have the same underlying algebraic structure. We introduce a seniority eigenstate configuration interaction in which the wave function is constrained to have good fixed local seniority for each paired orbital, by which we mean we partition orbitals into a pairing set with seniority zero, and a spin set with seniority one. Here, we show how to build the effective Hamiltonian for this ansatz, and demonstrate that high-seniority wave functions have unexpectedly excellent accuracy for strongly correlated fermionic systems, with accuracy competitive with or better than seniority zero for the Hubbard model and for the dissociation of the nitrogen molecule.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Emulators for Scarce and Noisy Data: Application to Auxiliary-Field Diffusion Monte Carlo for Neutron Matter

Understanding the equation of state (EOS) of pure neutron matter is necessary for interpreting multimessenger observations of neutron stars. Reliable data analyses of these observations require well-quantified uncertainties for the EOS input, ideally propagating uncertainties from nuclear interactions directly to the EOS. This, however, requires calculations of the EOS for a prohibitively larger number of nuclear Hamiltonians, solving the nuclear many-body problem for each one. Quantum Monte Carlo methods, such as auxiliary-field diffusion Monte Carlo (AFDMC), provide precise and accurate results for the neutron matter EOS, but they are very computationally expensive, making them unsuitable for the fast evaluations necessary for uncertainty propagation. Here, we employ parametric matrix models to develop fast emulators for AFDMC calculations of neutron matter and use them to directly propagate uncertainties of coupling constants in the Hamiltonian to the EOS. As these uncertainties include estimates of the effective field theory truncation uncertainty, this approach provides robust uncertainty estimates for use in astrophysical data analyses. In conclusion, this Letter will enable novel applications such as using astrophysical observations to put constraints on coupling constants for nuclear interactions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Clifford Circuit-Based Heuristic Optimization of Fermion-To-Qubit Mappings

Simulation of interacting Fermionic Hamiltonians is one of the most promising applications of quantum computers. However, the feasibility of analyzing Fermionic systems with a quantum computer hinges on the efficiency of Fermion-to-qubit mappings that encode nonlocal Fermionic degrees of freedom in local qubit degrees of freedom. While recent studies have highlighted the importance of designing Fermion-to-qubit mappings that are tailored to specific problem Hamiltonians, the methods proposed so far either are restricted to a narrow class of mappings or they use computationally expensive and unscalable brute-force search algorithms. Here, in this work, we address this challenge by designing a heuristic numerical optimization framework for Fermion-to-qubit mappings. To this end, we first translate the Fermion-to-qubit mapping problem to a Clifford circuit optimization problem and then use simulated annealing to optimize the average Pauli weight of the problem Hamiltonian. For all Fermionic Hamiltonians we have considered, the numerically optimized mappings outperform their conventional counterparts, including ternary-tree-based mappings that are known to be optimal for single creation and annihilation operators. We find that our optimized mappings yield between 15% and 40% improvements on the average Pauli weight when the simulation Hamiltonian has an intermediate level of complexity. Most remarkably, the optimized mappings improve the average Pauli weight for 6 × 6 nearest-neighbor hopping and Hubbard models by more than 40% and 20%, respectively. Surprisingly, we also find specific interaction Hamiltonians for which the optimized mapping outperforms any ternary-tree-based mapping. Our results establish heuristic numerical optimization as an effective method for obtaining mappings tailored for specific Fermionic Hamiltonian.

Hamiltonians↗
DOE OSTI2024

Hamiltonian learning using machine-learning models trained with continuous measurements

Here, we build upon recent work on the use of machine-learning models to estimate Hamiltonian parameters using continuous weak measurement of qubits as input. We consider two settings for the training of our model: (1) supervised learning, where the weak-measurement training record can be labeled with known Hamiltonian parameters, and (2) unsupervised learning, where no labels are available. The first has the advantage of not requiring an explicit representation of the quantum state, thus potentially scaling very favorably to a larger number of qubits. The second requires the implementation of a physical model to map the Hamiltonian parameters to a measurement record, which we implement using an integrator of the physical model with a recurrent neural network to provide a model-free correction at every time step to account for small effects not captured by the physical model. We test our construction on a system of two qubits and demonstrate accurate prediction of multiple physical parameters in both the supervised context and the unsupervised context. We demonstrate that the model benefits from larger training sets, establishing that it is “learning,” and we show robustness regarding errors in the assumed physical model by achieving accurate parameter estimation in the presence of unanticipated single-particle relaxation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Trends of Neutron Skins and Radii of Mirror Nuclei from First Principles

The neutron skin of atomic nuclei impacts the structure of neutron-rich nuclei, the equation of state of nucleonic matter, and the size of neutron stars. Here we predict the neutron skin of selected light- and medium-mass nuclei using coupled-cluster theory and the auxiliary field diffusion Monte Carlo method with two- and three-nucleon forces from chiral effective field theory. We find a linear correlation between the neutron skin and the isospin asymmetry in agreement with the liquid-drop model and compare with data. We also extract the linear relationship that describes the difference between neutron and proton radii of mirror nuclei and quantify the effect of charge symmetry breaking terms in the nuclear Hamiltonian. In conclusion, our results for the mirror-difference charge radii and binding energies per nucleon agree with existing data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Basis light-front quantization approach to nucleon

We obtain the light-front wavefunctions for the nucleon in the valence quark Fock space from an effective Hamiltonian, which includes the transverse and longitudinal confinement and the one gluon exchange interaction with fixed coupling. The wavefunctions are generated by solving the eigenvalue equation in a basis light front quantization. Fitting the model parameters, the wavefunctions lead to good simultaneous description of electromagnetic form factors, radii, and parton distribution functions for the proton.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

An attempt to simulate laser-induced all-optical spin switching in a crystalline ferrimagnet

Interest in all-optical spin switching (AOS) is growing rapidly. The recent discovery of AOS in Mn 2 RuGa provides a much needed clean case of crystalline ferrimagnets for theoretical simulations. Here, we attempt to simulate it using the state-of-the-art first-principles method combined with the Heisenberg exchange model. We first compute the spin moments at two inequivalent manganese sites and then feed them into our model Hamiltonian. We employ an ultrafast laser pulse to switch the spins. We find that there is a similar optimal laser field amplitude to switch spins. However, we find that the exchange interaction has a significant effect on the system switchability. Weakening the exchange interaction could make the system unswitchable. This provides a crucial insight into the switching mechanism in ferrimagnets.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Effective many-body interactions in reduced-dimensionality spaces through neural network models

Accurately describing properties of challenging problems in physical sciences often requires complex mathematical models that are unmanageable to tackle head on. Therefore, developing reduced-dimensionality representations that encapsulate complex correlation effects in many-body systems is crucial to advance the understanding of these complicated problems. However, a numerical evaluation of these predictive models can still be associated with a significant computational overhead. To address this challenge, in this paper we discuss a combined framework that integrates recent advances in the development of active-space representations of coupled cluster (CC) downfolded Hamiltonians with neural network approaches. The primary objective of this effort is to train neural networks to eliminate the computationally expensive steps required for evaluating hundreds or thousands of Hugenholtz diagrams, which correspond to multidimensional tensor contractions necessary for evaluating a many-body form of downfolded effective Hamiltonians. Using small molecular systems (the H 2 O and HF molecules) as examples, we demonstrate that training neural networks employing effective Hamiltonians for a few nuclear geometries of molecules can accurately interpolate or extrapolate their forms to other geometrical configurations characterized by different intensities of correlation effects. We also discuss differences between effective interactions that define CC downfolded Hamiltonians with those of bare Hamiltonians defined by Coulomb interactions in the active spaces. Published by the American Physical Society 2024

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Classification of fragile topology enabled by matrix homotopy

Flat bands in twisted materials have attracted considerable attention due to the emergence of correlated phases that can be associated with the non-Wannier-representable nature of its single-particle states. Specifically, these bands can exhibit a class of topology that can be nullified by the addition of trivial bands, termed fragile topology, which has required an expansion of prior classification schemes. However, existing approaches for predicting fragile topology rely on momentum-space methods, e.g., Wilson loops, presenting a fundamental challenge for using fragile topology as a predictor of correlated phases in aperiodic systems, such as incommensurate twist angles in moiré materials. Here, we develop a ℤ 2 energy-resolved topological marker for classifying fragile phases using a system’s position-space description, enabling the direct classification of finite, disordered, and aperiodic materials. By translating the physical symmetries protecting the system’s fragile topological phase into matrix symmetries of the system’s Hamiltonian and position operators, we use matrix homotopy to construct our topological marker while simultaneously yielding a quantitative measure of topological robustness. We demonstrate our framework’s effectiveness in both a low-energy tight-binding model and a continuum photonic crystal model of 𝐶 2 ⁢𝒯-symmetric systems, and find that fragile topology can both persist under strong disorder and even exhibit disorder-induced reentrant phase transitions. Our photonic crystal results also demonstrate the robustness of fragile topology, and the applicability of our approach, to heterostructures lacking a bulk spectral gap. Overall, our framework serves as an efficient tool for elucidating fragile topology, offering guidance for the prediction and discovery of correlated phases in both crystalline and aperiodic materials.

Lee, Ki Young [Sandia National Laboratories (SNL-N↗
DOE OSTI2023

Modeling of standing wave RF cavities for tracking through multi-pass energy recovery linac

Short bunches, high current and multiple linac pass are all characteristics of Energy Recovery Linacs (ERLs), which may result in collective effects. They in turn, may affect the beam, degrading its quality, or even yield to instabilities causing a beam loss. To study and mitigate these effects one needs a numerical simulation code, that can take into account both the collective effects, as well as, particular ERL features, such as a multi-turn design that does not reach a steady state or the multiple passages of the beam through Radio-Frequency (RF) cavities at different energies. CODAL [1], a code developed by SOLEIL in collaboration with IJCLab, enables such studies. It is a 6 dimensional (6D) tracking code applying 'kicks' based on the integration of the local Hamiltonian for each element of the lattice. It is also capable of simulating space charge, wakefields and coherent synchrotron radiation. However, to correctly take into account the ERL dynamics, an upgrade had to be made to include the effect of a standing wave RF cavity in 6D. In this paper, we will concentrate on the implementation and benchmarking (with DESY’s tracking code ASTRA [2]) of both the longitudinal and the transverse models (by J.B. Rosenzweig and L. Serafini [3]), which we use to carry out tracking of fully analytical 6D RF cavity.

Bogacz, A.↗
DOE OSTI2025

SympGNNs: Symplectic Graph Neural Networks for identifying high-dimensional Hamiltonian systems and node classification

Existing neural network models to learn Hamiltonian systems, such as SympNets, although accurate in low-dimensions, struggle to learn the correct dynamics for high-dimensional many-body systems. Herein, we introduce Symplectic Graph Neural Networks (SympGNNs) that can effectively handle system identification in high-dimensional Hamiltonian systems, as well as node classification. SympGNNs combine symplectic maps with permutation equivariance, a property of graph neural networks. Specifically, we propose two variants of SympGNNs: (i) G-SympGNN and (ii) LA-SympGNN, arising from different parameterizations of the kinetic and potential energy. We demonstrate the capabilities of SympGNN on two physical examples: a 40-particle coupled Harmonic oscillator, and a 2000-particle molecular dynamics simulation in a two-dimensional Lennard-Jones potential. Furthermore, we demonstrate the performance of SympGNN in the node classification task, achieving accuracy comparable to the state-of-the-art. Finally, we also empirically show that SympGNN can overcome the oversmoothing and heterophily problems, two key challenges in the field of graph neural networks.

Deep learning↗
DOE OSTI2021

K-Shell photoabsorption in Si 11+ : Relativistic contributions via Breit-Pauli R-matrix calculations

As a part of the investigation of the entire Si isonuclear sequence for x-ray spectral diagnostics, we focus on the Li-like Si 11+ ion, a stable component that features prominently in x-ray astrophysical spectra. In this work, we perform R-matrix calculations for the photoabsorption cross section of Si 11+ including relativistic contributions via the use of a Breit-Pauli Hamiltonian. Relativistic effects—predominantly spin-orbit splitting of resonances and mass-velocity and one-body Darwin global shifts of energies— are shown to be tractable and of importance for accuracy in x-ray spectral modeling data banks.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Luther-Emery liquid and dominant singlet superconductivity in the hole-doped Haldane spin-1 chain

We investigate the pairing tendencies in the hole-doped Haldane spin-1 chain. To allow for doping, we extend the original spin chain Hamiltonian into a fermionic model involving a two-orbital Hubbard chain at intermediate or strong repulsive interaction strengths U and for degenerate orbitals. At half filling and large U, the ferromagnetic Hund's coupling, J H , generates effective spin-1 moments, with antiferromagnetic correlations between sites. Using large-scale density matrix renormalization group calculations, we accurately study the system's behavior under light hole-doping. For U = 1.6 in units of the noninteracting bandwidth and for J H /U ≳ 0.275, we find that singlet pairing dominates the long-distance physics, establishing this system as a promising platform for repulsively mediated superconductivity. We provide concrete examples of materials that could realize the physics described here. We also provide evidence that the system approaches a Luther-Emery liquid state at large system sizes, reminiscent of the behavior of doped one-orbital two-leg ladders at weak coupling, which also have superconducting tendencies. The numerically calculated central charge approaches one in the thermodynamic limit, indicating a single gapless mode as is expected for the Luther-Emery state. Exponents characterizing the power-law decays of singlet pair-pair and charge density-density correlations are determined, and found to approximately satisfy the Luther-Emery identity.

1-dimensional systems↗
DOE OSTI2024

Spin crossover transition driven by pressure: Barocaloric applications

This article describes a mean-field theoretical model for Spin-Crossover (SCO) materials and explores its implications. It is based on a simple Hamiltonian that yields the high spin molar fraction as a function of temperature and pressure, as well as a temperature–pressure phase diagram for the SCO transition. In order to test the model, it was compared with the giant Barocaloric Effect (BCE) of the SCO material [FeL 2 ][B 4 ] 2 . Furthermore, we found that optical phonons are responsible for 92% of the total barocaloric entropy change. DFT calculations successively indicates that, as expected, the majority of this effect can be traced to low frequencies modes of vibration (400 cm -1 ), associated to the Fe coordination.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Approximate CFTs and random tensor models

Abstract A key issue in both the field of quantum chaos and quantum gravity is an effective description of chaotic conformal field theories (CFTs), that is CFTs that have a quantum ergodic limit. We develop a framework incorporating the constraints of conformal symmetry and locality, allowing the definition of ensembles of ‘CFT data’. These ensembles take on the same role as the ensembles of random Hamiltonians in more conventional quantum ergodic phases of many-body quantum systems. To describe individual members of the ensembles, we introduce the notion of approximate CFT, defined as a collection of ‘CFT data’ satisfying the usual CFT constraints approximately, i.e. up to small deviations. We show that they generically exist by providing concrete examples. Ensembles of approximate CFTs are very natural in holography, as every member of the ensemble is indistinguishable from a true CFT for low-energy probes that only have access to information from semi-classical gravity. To specify these ensembles, we impose successively higher moments of the CFT constraints. Lastly, we propose a theory of pure gravity in AdS 3 as a random matrix/tensor model implementing approximate CFT constraints. This tensor model is the maximum ignorance ensemble compatible with conformal symmetry, crossing invariance, and a primary gap to the black-hole threshold. The resulting theory is a random matrix/tensor model governed by the Virasoro 6j-symbol.

Physics↗
DOE OSTI2020

Slow manifold reduction for plasma science

The classical Chapman–Enskog procedure admits a substantial geometrical generalization known as slow manifold reduction. This generalization provides a paradigm for deriving and understanding most reduced models in plasma physics that are based on controlled approximations applied to problems with multiple timescales. In this Review we develop the theory of slow manifold reduction with a plasma physics audience in mind. In particular we illustrate (a) how the slow manifold concept may be used to understand breakdown of a reduced model over sufficiently-long time intervals, and (b) how a discrete-time analogue of slow manifold theory provides a useful framework for developing implicit integrators for temporally-stiff plasma models. For readers with more advanced mathematical training we also use slow manifold reduction to explain the phenomenon of inheritance of Hamiltonian structure in dissipation-free reduced plasma models. Various facets of the theory are illustrated in the context of the Abraham–Lorentz model of a single charged particle experiencing its own radiation drag. As a culminating example we derive the slow manifold underlying kinetic quasineutral plasma dynamics up to first-order in perturbation theory. This first-order result incorporates several physical effects associated with small deviations from exact charge neutrality that lead to slow drift away from predictions based on the leading-order approximation n e = Z i n i .

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗