Search NASA⌕ Search

SEARCH · Search NASA

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Symplectic machine learning model for fast simulation of space-charge effects

Symplectic simulation of space-charge effects is crucial for the design and operation of high-intensity particle accelerators. Traditional methods for simulating these effects are often computationally expensive, resulting in significant overhead. In this work, we introduce a generative model based on a U-Net architecture within a generative adversarial network framework to efficiently simulate space-charge effects. The model is trained to predict the transverse multiparticle space-charge Hamiltonian, which can be physically computed using a gridless spectral method. The one-step symplectic transverse transfer map for the particles is then obtained by differentiating the predicted Hamiltonian. Benchmarking results demonstrate that this generative model achieves an order of magnitude higher computational efficiency compared to the spectral method, providing a highly efficient alternative for simulating space-charge effects with a large number of particles. By maintaining symplecticity, the model effectively preserves the phase-space structure and mitigates nonphysical errors in long-term simulations. This model has been integrated into jutrack, a novel autodifferentiable accelerator modeling code developed in the julia programming language.

Beam code development & simulation techniques↗
DOE OSTI2020

Origin of mean-field behavior in an elastic Ising model

Simple elastic models of spin-crossover compounds are known empirically to exhibit classical critical behavior. Here, we demonstrate how the long-range interactions responsible for this behavior arise naturally upon integrating out mechanical fluctuations of such a model. A mean-field theory applied to the resulting effective Hamiltonian quantitatively accounts for both thermodynamics and kinetics observed in computer simulations, including a barrier to magnetization reversal that grows extensively with system size. For nanocrystals, which break translational symmetry, a straightforward extension of mean-field theory yields similarly accurate results.

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

Topological obstructed atomic limit insulators by annihilating Dirac fermions

We show that annihilating a pair of Dirac fermions implies a topological transition from the critical semimetallic phase to an obstructed atomic limit insulator phase instead of a trivial insulator. This is shown to happen because of branch cuts in the phase of the wave functions, leading to nontrivial Zak phase along certain directions. To this end, we study their ${\mathbb{Z}}_{2}$ invariant and also study the phase transition using entanglement entropy. We use low-energy Hamiltonians and numerical result from model systems to show this effect. These transitions are observed in realistic materials, including strained graphene and buckled honeycomb group V (Sb/As).

36 MATERIALS SCIENCE↗
DOE OSTI2023

Magnetic ground state and perturbations of the distorted kagome Ising metal TmAgGe

Here, we present the magnetic orders and excitations of the distorted kagome intermetallic magnet TmAgGe. Using neutron single crystal diffraction we identify the propagation vectors k = ($\frac{1}{2}$ 0 0) and k = (0 0 0) and determine the magnetic structures of the zero-field and magnetic field-induced phases for H along the $\mathcal{a}$ and [–110] crystal directions. We determine the experimental magnetic field- temperature (H, T)-phase diagram and reproduce it by Monte Carlo simulations of an effective spin exchange Hamiltonian for one distorted kagome layer. Our model includes a strong axial single-ion anisotropy and significantly smaller exchange couplings, which span up to the third-nearest neighbors within the layer. Single crystal inelastic neutron scattering (INS) measurements reveal an almost flat, only weakly dispersive mode around 7 meV that we use alongside bulk magnetization data to deduce the crystal-electric field (CEF) scheme for the Tm 3+ ions. Random phase approximation (RPA) calculations based on the determined CEF wave functions of the two lowest quasidoublets enable an estimation of the interlayer coupling that is compatible with the experimental INS spectra. No evidence for low-energy spin waves associated to the magnetic order was found, which is consistent with the strongly Ising nature of the ground state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Derivation of low-energy Hamiltonians for heavy-fermion materials

Here, by utilizing a multiorbital periodic Anderson model with parameters obtained from ab initio band structure calculations, combined with degenerate perturbation theory, we derive effective Kondo-Heisenberg and spin Hamiltonians that capture the interaction among the effective magnetic moments. This derivation encompasses fluctuations via both nonmagnetic 4⁢𝑓 0 and magnetic 4⁢𝑓 2 virtual states, and its accuracy is confirmed through comparison with experimental data obtained from CeIn 3 . The significant agreement observed between experimental results and theoretical predictions underscores the potential of deriving minimal models from first-principles calculations for achieving a quantitative description of 4⁢𝑓 materials. Moreover, our microscopic derivation unveils the underlying origin of anisotropy in the exchange interaction between Kramers doublets, shedding light on the conditions under which this anisotropy may be weak compared to the isotropic contribution.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Nonadiabatic Dynamics in a Continuous Circularly Polarized Laser Field with Floquet Phase-Space Surface Hopping

Non-adiabatic chemical reactions involving continuous circularly polarized light (cw CPL) have not attracted as much attention as dynamics in unpolarized/linearly polarized light. However, including circularly (in contrast to linearly) polarized light allows one to effectively introduce a complex-valued time-dependent Hamiltonian, which offers a new path for control or exploration through the introduction of Berry forces. Here, we investigate several inexpensive semiclassical approaches for modeling such nonadiabatic dynamics in the presence of a time-dependent complex-valued Hamiltonian, beginning with a straightforward instantaneous adiabatic fewest-switches surface hopping (IA-FSSH) approach (where the electronic states depend on position and time), continuing to a standard Floquet fewest switches surface hopping (F-FSSH) approach (where the electronic states depend on position and frequency), and ending with an exotic Floquet phase-space surface hopping (F-PSSH) approach (wherethe electronic states depend on position, frequency, and momentum). Using a set of model systems with time-dependent complex-valued Hamiltonians, we show that the Floquet phase- space adiabats are the optimal choice of basis as far as accounting for Berry phase effects and delivering accuracy. Furthermore, the F-PSSH algorithm sets the stage for modeling nonadiabatic dynamics under strong externally pumped circular polarization in the future.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Anisotropic magneto-resistivity and magnetocaloric effect in DyAl 2

Here, in this study, we experimentally and theoretically investigate the correlation between the anisotropic magnetic resistivity and magnetocaloric effect in DyAl 2 single crystals. DyAl 2 crystallizes in the C15 Laves phase structure with cubic symmetry. While some earlier studies revealed that the isothermal entropy change in dialuminides follows a similar trend as the electrical resistivity change as a function of temperature and magnetic field, the correlation between anisotropic behavior of these two physical parameters is yet to be explored to the best of our knowledge. To address this gap, we measured electrical resistivity of DyAl 2 single crystals along two different directions in zero and applied magnetic fields and compared the experimental results with our theoretical model. For the theoretical analysis, we employed a model Hamiltonian in the mean-field approximation, considering the exchange interaction, Zeeman effect, and crystalline electric field associated with the cubic symmetry. Our findings reveal a significant dependence of DyAl 2 resistivity on the direction of the applied magnetic field, in agreement with our theoretical results. These outcomes emphasize the interplay between magnetocaloric effect and magneto-resistivity, underscoring the potential of the magnetocaloric effect as a valuable tool for gaining deeper insights into basic physical properties including electron transport behavior.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Influence of non-adiabatic effects on linear absorption spectra in the condensed phase: Methylene blue

Modeling linear absorption spectra of solvated chromophores is highly challenging as contributions are present both from coupling of the electronic states to nuclear vibrations and from solute–solvent interactions. In systems where excited states intersect in the Condon region, significant non-adiabatic contributions to absorption line shapes can also be observed. Here, we introduce a robust approach to model linear absorption spectra accounting for both environmental and non-adiabatic effects from first principles. This model parameterizes a linear vibronic coupling (LVC) Hamiltonian directly from energy gap fluctuations calculated along molecular dynamics (MD) trajectories of the chromophore in solution, accounting for both anharmonicity in the potential and direct solute–solvent interactions. The resulting system dynamics described by the LVC Hamiltonian are solved exactly using the thermalized time-evolving density operator with orthogonal polynomials algorithm (T-TEDOPA). The approach is applied to the linear absorption spectrum of methylene blue in water. We show that the strong shoulder in the experimental spectrum is caused by vibrationally driven population transfer between the bright S1 and the dark S2 states. The treatment of the solvent environment is one of many factors that strongly influence the population transfer and line shape; accurate modeling can only be achieved through the use of explicit quantum mechanical solvation. The efficiency of T-TEDOPA, combined with LVC Hamiltonian parameterizations from MD, leads to an attractive method for describing a large variety of systems in complex environments from first principles.

Dunnett, Angus J. (ORCID:0000000285797826)↗
DOE OSTI2024

Quantifying Quantum Chaos through Microcanonical Distributions of Entanglement

A characteristic feature of “quantum chaotic” systems is that their eigenspectra and eigenstates display universal statistical properties described by random matrix theory (RMT). However, eigenstates of local systems also encode structure beyond RMT. To capture this feature, we introduce a framework that allows us to compare the properties of eigenstates in local systems with those of pure random states. In particular, our framework defines a notion of distance between quantum state ensembles that utilizes the Kullback-Leibler divergence to compare the microcanonical distribution of entanglement entropy (EE) of eigenstates with a reference RMT distribution generated by pure random states (with appropriate constraints). This notion gives rise to a quantitative metric for quantum chaos that not only accounts for averages of the distributions but also higher moments. The differences in moments are compared on a highly resolved scale set by the standard deviation of the RMT distribution, which is exponentially small in system size. As a result, the metric can distinguish between chaotic and integrable behaviors and, in addition, quantify and compare the of chaos (in terms of proximity to RMT behavior) between two systems that are assumed to be chaotic. We implement our framework in local, minimally structured, Floquet random circuits, as well as a canonical family of many-body Hamiltonians, the mixed-field Ising model (MFIM). Importantly, for Hamiltonian systems, we find that the reference random distribution must be appropriately constrained to incorporate the effect of energy conservation in order to describe the ensemble properties of midspectrum eigenstates. The metric captures deviations from RMT across all models and parameters, including those that have been previously identified as strongly chaotic, and for which other diagnostics of chaos such as level spacing statistics look strongly thermal. In Floquet circuits, the dominant source of deviations is the second moment of the distribution, and this persists for all system sizes. For the MFIM, we find significant variation of the KL divergence in parameter space. Notably, we find a small region where deviations from RMT are minimized, suggesting that “maximally chaotic” Hamiltonians may exist in fine-tuned pockets of parameter space. Published by the American Physical Society 2024

Physics↗
DOE OSTI2024

Deformed Fredkin model for the ν = 5 / 2 Moore-Read state on thin cylinders

We propose a frustration-free model for the Moore-Read quantum Hall state on sufficiently thin cylinders with circumferences ≲ 7 magnetic lengths. While the Moore-Read Hamiltonian involves complicated long-range interactions between triplets of electrons in a Landau level, our effective model is a simpler one-dimensional chain of qubits with deformed Fredkin gates. We show that the ground state of the Fredkin model has high overlap with the Moore-Read wave function and accurately reproduces the latter's entanglement properties. Moreover, we demonstrate that the model captures the dynamical response of the Moore-Read state to a geometric quench, induced by suddenly changing the anisotropy of the system. We elucidate the underlying mechanism of the quench dynamics and show that it coincides with the linearized bimetric field theory. The minimal model introduced here can be directly implemented as a first step towards quantum simulation of the Moore-Read state, as we demonstrate by deriving an efficient circuit approximation to the ground state and implementing it on an IBM quantum processor. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Variational Adiabatic Gauge Transformation on Real Quantum Hardware for Effective Low-Energy Hamiltonians and Accurate Diagonalization

Effective low-energy theories represent powerful theoretical tools to reduce the complexity in modeling interacting quantum many-particle systems. However, common theoretical methods rely on perturbation theory, which limits their applicability to weak interactions. Here we introduce the Variational Adiabatic Gauge Transformation (VAGT), a nonperturbative hybrid quantum algorithm that can use nowadays quantum computers to learn the variational parameters of the unitary circuit that brings the Hamiltonian to either its block-diagonal or full-diagonal form. If a Hamiltonian can be diagonalized via a shallow quantum circuit, then VAGT can learn the optimal parameters using a polynomial number of runs. The accuracy of VAGT is tested through numerical simulations, as well as simulations on Rigetti and IonQ quantum computers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Self-consistent effective Hamiltonian theory for fermionic many-body systems

Using a separable many-body variational wavefunction, we formulate a self-consistent effective Hamiltonian theory for fermionic many-body system. The theory is applied to the two-dimensional (2D) Hubbard model as an example to demonstrate its capability and computational effectiveness. Most remarkably for the Hubbard model in 2D, a highly unconventional quadruple-fermion non-Cooper pair order parameter is discovered.

Physics↗
DOE OSTI2025

Connecting relativistic density functional theory to microscopic calculations

The development of systematic effective field theories (EFTs) for nuclear forces and advances in solving the nuclear many-body problem have greatly improved our understanding of dense nuclear matter and the structure of finite nuclei. For global nuclear calculations, density functional theories (DFTs) have been developed to reduce the complexity and computational cost required in describing nuclear systems. However, DFT often makes approximations and assumptions about terms included in the functional, which may introduce systematic uncertainties compared to microscopic calculations using EFTs. In this work, we investigate possible avenues of improving nuclear DFT using nonlinear relativistic mean-field (RMF) theory. We explore the impact of RMF model extensions by fitting the nonlinear RMF model to predictions of nuclear matter and selected closed-shell nuclei using four successful chiral EFT Hamiltonians. We find that these model extensions are impactful and important in capturing the physics present within chiral Hamiltonians, particularly for charge radii and neutron skins of closed-shell nuclei. However, there are additional effects that are not captured within the RMF model, particularly within the isoscalar sector of RMF theory. Additional model extensions and the reliability of the nonlinear RMF model are discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Effect of the inversion symmetry breaking on the orbital Hall effect: A model study

The orbital Hall effect (OHE) is the transverse flow of orbital moment in a solid in response to an applied electric field, analogous to the flow of spin moment in the spin Hall effect (SHE). Although the effect has not been directly observed, there is ample indirect evidence for its existence in a number of experiments. Here, we show that the OHE is enhanced in solids with broken inversion symmetry, which may be more suitable to observe the effect. The mechanism of the OHE is fundamentally different in solids with inversion symmetry, where the orbital moment is quenched in the Brillouin zone (BZ), from that in a solid with broken inversion symmetry, where an intrinsic orbital moment is already present, the motion of which under the applied electric field could lead to a robust OHE. Using a tight-binding model Hamiltonian of a simple cubic lattice with two atoms in the unit cell, we study the effect of the inversion symmetry breaking on the OHE. We show that with the increase in the strength of the broken symmetry, the magnitude of the intrinsic orbital moment in the Brillouin zone increases. This, in turn, enhances the orbital Hall conductivity, in particular, the part that is directly proportional to the orbital moment in the BZ, which we call the “noncentrosymmetric contribution.” If the spin-orbit coupling is present, which couples the orbital and spin moments, the OHE leads to the SHE, which also becomes enhanced by the broken inversion symmetry. Furthermore, our work has important implications for experimenters, suggesting that noncentrosymmetric solids may be more suitable for direct observation of the OHE.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Interplay between disorder, local relaxation, and collective behavior for an ensemble of emitters outside versus inside a cavity

The interplay between collective optical response and molecular static and dynamic disorder is studied using simple effective Hamiltonians for an ensemble of two-level emitters inside and outside a single-mode cavity. We model environmental disorder by randomly modulating the molecular transition frequencies and the coupling between the emitters and the electromagnetic field. We also consider the effects of intermolecular interactions and orientational disorder. We investigate how these effects lead to new features in the steady-state absorption (outside the cavity), transmission spectra (inside the cavity), and the yield of local molecular processes such as a unimolecular reaction. Outside the cavity, the collective behavior is manifested in the linewidth of the steady-state absorption, the emission spectrum, and the local chemical yield. Inside the cavity, however, the collective behavior primarily determines the Rabi splitting. The effects of intermolecular interactions under orientational disorder are also studied. For the most part, for all types of disorder, if we increase disorder, we find a reduction in the collective nature of the molecular response (smaller effective N) and therefore the Rabi splitting contraction occurs with orientational disorder. Furthermore, we find that static disorder is more destructive to collective behavior than dynamic disorder.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Magnetic field-temperature phase diagram of the spin-$\frac{1}{2}$ triangular lattice antiferromagnet KYbSe 2

A quantum spin liquid (QSL) is a state of matter characterized by fractionalized quasiparticle excitations, quantum entanglement, and a lack of long-range magnetic order. However, QSLs have evaded definitive experimental observation. Several Yb 3+ -based triangular lattice antiferromagnets with effective 𝑆 = $\frac{1}{2}$ have been suggested to stabilize the QSL state as the ground state. Here, in this work, we build a comprehensive magnetic temperature phase diagram of a high-quality single crystalline KYbSe 2 via heat capacity and magnetocaloric effect down to 30 mK with magnetic field applied along the 𝑎 axis. At zero magnetic field, we observe the magnetic long-range order at 𝑇 N =0.29 K entering 120 degrees ordered state in heat capacity, consistent with neutron scattering studies. Analysis of the low-temperature (𝑇) specific heat (𝐶) at zero magnetic field indicates linear 𝑇 dependence of 𝐶/𝑇 and a broad hump of 𝐶/𝑇 in the proximate QSL region above 𝑇 N . By applying magnetic field, we observe the up-up-down phase with 1/3 magnetization plateau and oblique phases, in addition to two new phases. These observations strongly indicate that while KYbSe 2 closely exhibits characteristics resembling an ideal triangular lattice, deviations may exist, such as the effect of the next-nearest-neighbor exchange interaction, calling for careful consideration for spin Hamiltonian modeling. Further investigations into tuning parameters, such as chemical pressure, could potentially induce an intriguing QSL phase in the material.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Effective Hamiltonians derived from equation-of-motion coupled-cluster wave functions: Theory and application to the Hubbard and Heisenberg Hamiltonians

Effective Hamiltonians, which are commonly used for fitting experimental observables, provide a coarse-grained representation of exact many-electron states obtained in quantum chemistry calculations; however, the mapping between the two is not trivial. In this contribution, we apply Bloch’s formalism to equation-of-motion coupled-cluster (EOM-CC) wave functions to rigorously derive effective Hamiltonians in the Bloch’s and des Cloizeaux’ forms. We report the key equations and illustrate the theory by application to systems with two or three unpaired electrons, which give rise to electronic states of covalent and ionic characters. We show that the Hubbard and Heisenberg Hamiltonians can be extracted directly from the so-obtained effective Hamiltonians. By establishing a quantitative connection between many-body states and simple models, the approach facilitates the analysis of the correlated wave functions. We propose a simple diagnostic for assessing the validity of the model space choice based on the overlaps between the target- and model-space states. Finally, artifacts affecting the quality of electronic structure calculations such as spin contamination are also discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Exploring the nexus of many-body theories through neural network techniques: the tangent model

Abstract In this paper, we present a physically informed neural network (NN) representation of the effective interactions associated with coupled-cluster downfolding models to describe chemical systems and processes. The NN representation not only allows us to evaluate the effective interactions efficiently for various geometrical configurations of chemical systems corresponding to various levels of complexity of the underlying wave functions, but also reveals that the bare and effective interactions are related by a tangent function of some latent variables. We refer to this characterization of the effective interaction as a tangent model. We discuss the connection between this tangent model for the effective interaction with the previously developed theoretical analysis that examines the difference between the bare and effective Hamiltonians in the corresponding active spaces.

97 MATHEMATICS AND COMPUTING↗