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Results for “Pairing Hamiltonian”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Mechanical cosmology: Simulating scalar fluctuations in expanding universes using synthetic mechanical lattices

Inspired by recent advances in observational astrophysics and continued explorations in the field of analog gravity, we discuss the prospect of simulating models of cosmology within the context of synthetic mechanical lattice experiments. We focus on the physics of expanding universe scenarios described by the Friedmann-Lemaître-Robertson-Walker (FLRW) metric. Specifically, quantizing scalar fluctuations in a background FLRW spacetime leads to a quadratic bosonic Hamiltonian with temporally varying pair production terms. Here we present a mapping that provides a one-to-one correspondence between these classes of cosmology models and feedback-coupled mechanical oscillators. As proof of principle, we then perform experiments on a synthetic mechanical lattice composed of such oscillators. We simulate two different FLRW expansion scenarios with universes dominated by vacuum energy and matter and discuss our experimental results. Published by the American Physical Society 2025

Rhyno, Brendan (ORCID:0000000235266998)↗
DOE OSTI2022

Simultaneous fermion and exciton condensations from a model Hamiltonian

Fermion-exciton condensation in which both fermion-pair (i.e., superconductivity) and exciton condensations occur simultaneously in a single coherent quantum state has recently been conjectured to exist. Here, we capture the fermion-exciton condensation through a model Hamiltonian that can recreate the physics of this new class of highly correlated condensation phenomena. We demonstrate that the Hamiltonian generates the large-eigenvalue signatures of fermion-pair and exciton condensations for a series of states with increasing particle numbers. The results confirm that the dual-condensate wave function arises from the entanglement of fermion-pair and exciton wave functions, which we previously predicted in the thermodynamic limit. Furthermore, this model Hamiltonian—generalizing well-known model Hamiltonians for either superconductivity or exciton condensation—can explore a wide variety of condensation behavior. It provides significant insights into the required forces for generating a fermion-exciton condensate, which will likely be invaluable for realizing such condensations in realistic materials with applications from superconductors to excitonic materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Size-Transferable Prediction of Excited State Properties for Molecular Assemblies with a Machine Learning Exciton Model

Computational modeling of the excited states of molecular aggregates faces significant computational challenges and size heterogeneity. Current machine learning (ML) models, typically trained on specific-sized aggregates, struggle with scalability. We found that the exciton model Hamiltonian of large aggregates can be decomposed into dimer pairs, allowing an ML model trained on dimers to reconstruct Hamiltonians for aggregates of any size. We also proposed a new method to address the phase-correction problem by introducing coupling terms’ approximations. Our model accurately predicted the excitation energies of the trimer and tetramer of perylene and tetracene and estimated S1 oscillator strengths of perylene aggregates. Leveraging our ML model, the optical gaps of nanosized perylene aggregates with up to 50 monomers are analyzed, qualitatively revealing the role of different couplings on their size dependency. Future work will explore transferability across different monomers to predict optical properties in heterogeneous assemblies.

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

Anomalous electrodynamics and quantum geometry in the Dirac-Harper model for a graphene bilayer

In this work, graphene bilayers with layer antisymmetric strains are studied using the Dirac-Harper model for a pair of single layer Dirac Hamiltonians coupled by a one-dimensional moiré-periodic interlayer tunneling amplitude. This model hosts low energy, nearly dispersionless bands near charge neutrality that support anomalous polarizations of its charge multipole distributions. These are analyzed introducing a generalized Berry curvature that encodes the field-induced dynamics of multipole fields allowed in a chiral medium with time reversal symmetry. The formulation identifies a reciprocity relation between responses to layer-symmetric and layer-antisymmetric in-plane electric fields and reveals momentum-space quantum oscillations produced by a spatial pattern of band inversions on the moiré scale.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Ideal weak topological insulator and protected helical saddle points

Here we report the design and observation of an ideal weak topological insulator in a quasi-one-dimensional bismuth halide, Bi 4 I 1.2 Br 2.8 . Via angle-resolved photoemission spectroscopy, we identify that Bi 4 I 1.2 Br 2.8 hosts topological surface states on the (100)′ side surface in the form of two anisotropic π-offset Dirac cones while topologically dark on the (001) top surface. The results fully determine a unique side-surface Hamiltonian and thereby identify two pairs of nondegenerate helical saddle points. The fact that both the surface Dirac and helical saddle points are in the global bulk band gap of 195 meV suggests the potential of this system to be a fertile ground for topological many-body physics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Fermionic mean-field theory as a tool for studying spin Hamiltonians

The Jordan–Wigner transformation permits one to convert spin 1/2 operators into spinless fermion ones, or vice versa. In some cases, it transforms an interacting spin Hamiltonian into a noninteracting fermionic one, which is exactly solved at the mean-field level. Even when the resulting fermionic Hamiltonian is interacting, its mean-field solution can provide surprisingly accurate energies and correlation functions. Furthermore, Jordan–Wigner is, however, only one possible means of interconverting spin and fermionic degrees of freedom. Here, we apply several such techniques to the XXZ and J 1 –J 2 Heisenberg models, as well as to the pairing or reduced Bardeen–Cooper–Schrieffer Hamiltonian, with the aim of discovering which of these mappings is most useful in applying fermionic mean-field theory to the study of spin Hamiltonians.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Quantum Simulation of Molecular Electronic States with a Transcorrelated Hamiltonian: Higher Accuracy with Fewer Qubits

Simulation of electronic structure is one of the most promising applications on noisy intermediate-scale quantum (NISQ) era devices. However, NISQ devices suffer from a number of challenges like limited qubit connectivity, short coherence times, and sizable gate error rates. Thus, desired quantum algorithms should require shallow circuit depths and low qubit counts to take advantage of these devices. Here, we attempt to reduce quantum resource requirements for molecular simulations on a quantum computer while maintaining the desired accuracy with the help of classical quantum chemical theories of canonical transformation and explicit correlation. In this work, compact ab initio Hamiltonians are generated classically, in the second quantized form, through an approximate similarity transformation of the Hamiltonian with (a) an explicitly correlated two-body unitary operator with generalized pair excitations that remove the Coulombic electron–electron singularities from the Hamiltonian and (b) a unitary one-body operator to efficiently capture the orbital relaxation effects required for accurate description of the excited states. The resulting transcorrelated Hamiltonians are able to describe both the ground and the excited states of molecular systems in a balanced manner. Using the variational quantum eigensolver (VQE) method based on the unitary coupled cluster with singles and doubles (UCCSD) ansatz and only a minimal basis set (ANO-RCC-MB), we demonstrate that the transcorrelated Hamiltonians can produce ground state energies comparable to the reference CCSD energies with the much larger cc-pVTZ basis set. This leads to a reduction in the number of required CNOT gates by more than 3 orders of magnitude for the chemical species studied in this work. Furthermore, using the quantum equation of motion (qEOM) formalism in conjunction with the transcorrelated Hamiltonian, we are able to reduce the deviations in the excitation energies from the reference EOM-CCSD/cc-pVTZ values by an order of magnitude. In conclusion, the transcorrelated Hamiltonians developed here are Hermitian and contain only one- and two-body interaction terms and thus can be easily combined with any quantum algorithm for accurate electronic structure simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1990

Charge transfer polarisation wave and carrier pairing in the high T(sub c) copper oxides

The High T(sub c) oxides are highly polarizable materials and are charge transfer insulators. The charge transfer polarization wave formalism is developed in these oxides. The dispersion relationships due to long range dipole-dipole interaction of a charge transfer dipole lattice are obtained in 3-D and 2-D. These are high frequency bosons and their coupling with carriers is weak and antiadiabatic in nature. As a result, the mass renormalization of the carriers is negligible in complete contrast to conventional electron-phonon interaction, that give polarons and bipolarons. Both bound and superconducting pairing is discussed for a model Hamiltonian valid in the antiadiabatic regime, both in 3-D and 2-D. The stability of the charge transfer dipole lattice has interesting consequences that are discussed.

Chakraverty, B. K.↗
DOE OSTI2022

The 1 S 0 Pairing Gap in Neutron Matter

We report ab initio calculations of the S wave pairing gap in neutron matter calculated using realistic nuclear Hamiltonians that include two- and three-body interactions. We use a trial state, properly optimized to capture the essential pairing correlations, from which we extract ground state properties by means of auxiliary field diffusion Monte Carlo simulations. We extrapolate our results to the thermodynamic limit by studying the finite-size effects in the symmetry-restored projected Bardeen-Cooper-Schrieffer (PBCS) theory and compare our results to other ab initio studies done in the past. Our quantum Monte Carlo results for the pairing gap show a modest suppression with respect to the mean-field BCS values. These results can be connected to cold atom experiments, via the unitarity regime where fermionic superfluidity assumes a unified description, and they are important in the prediction of thermal properties and the cooling of neutron stars.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1995

Boson mapping techniques applied to constant gauge fields in QCD

Pairs of coordinates and derivatives of the constant gluon modes are mapped to new gluon-pair fields and their derivatives. Applying this mapping to the Hamiltonian of constant gluon fields results for large coupling constants into an effective Hamiltonian which separates into one describing a scalar field and another one for a field with spin two. The ground state is dominated by pairs of gluons coupled to color and spin zero with slight admixtures of color zero and spin two pairs. As color group we used SU(2).

Hess, Peter Otto↗
DOE OSTI2021

Reducing Qubit Requirements while Maintaining Numerical Precision for the Variational Quantum Eigensolver: A Basis-Set-Free Approach

We present a basis-set-free approach to the variational quantum eigensolver using an adaptive representation of the spatial part of molecular wave functions.Our approach directly determines system-specific representations of qubit Hamiltonians while fully omitting globally defined basis sets. In this work, we use directly determined pair-natural orbitals on the level of second-order perturbation theory. This results in compact qubit Hamiltonians with high numerical accuracy. We demonstrate initial applications with compact Hamiltonians on up to 22 qubits where conventional representation would for the same systems require 40–100 or more qubits. Here, we further demonstrate reductions in the quantum circuits through the structure ofthe pair-natural orbitals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Component-Level Inverse Design of Transmon Qubits Using Neural Networks

Designing a superconducting qubit to realize specific Hamiltonian parameters typically requires iterating through a time and compute-intensive forward loop in which the designer chooses a layout geometry, simulates it, extracts circuit parameters such as capacitances, and refines the geometry. We study the inverse version of this task using a neural-network workflow that maps target Hamiltonian parameters directly to component-level layout parameters, which we subsequently demonstrate on a planar transmon layout. During training, we pair the inverse model with a frozen forward surrogate model and evaluate the loss in Hamiltonian space rather than in layout-parameter space. In validation against a conventional EM solver, 97% of generated designs produce usable geometries, and the inverse-plus-surrogate pipeline reaches mean percent errors of 0.73% for qubit frequency and 1.58% for anharmonicity, comparable to or below the fabrication and simulation-to-measurement uncertainty expected for academic-process transmon devices of this type. A single pipeline query takes ~60 ms on CPU, versus ~2 min for a conventional EM capacitance extraction on the same hardware, a speedup of approximately 2,000x. Batching minimizes the AI model inference overhead, reducing the runtime to 3.1 microseconds per sample on CPU and 2.6 microseconds per sample on GPU at a batch size of 2048, resulting in speedups of 3.9 x 10^7 and 4.6 x 10^7, respectively, relative to a single conventional CPU EM extraction. Our results indicate that component-level inverse design usefully extends and complements conventional EM simulation, including for small datasets on the order of 1,000 samples.

Seidel, Olivia [Fermilab; Texas U., Arlington]↗
DOE OSTI2024

Determining the N -Representability of a Reduced Density Matrix via Unitary Evolution and Stochastic Sampling

The N-representability problem consists in determining whether, for a given p-body matrix, there exists at least one N-body density matrix from which the p-body matrix can be obtained by contraction, that is, if the given matrix is a p-body reduced density matrix (p-RDM). The knowledge of all necessary and sufficient conditions for a p-body matrix to be N-representable allows the constrained minimization of a many-body Hamiltonian expectation value with respect to the p-body density matrix and, thus, the determination of its exact ground state. However, the number of constraints that complete the N-representability conditions grows exponentially with system size, and hence, the procedure quickly becomes intractable for practical applications. This work introduces a hybrid quantum-stochastic algorithm to effectively replace the N-representability conditions. The algorithm consists of applying to an initial N-body density matrix a sequence of unitary evolution operators constructed from a stochastic process that successively approaches the reduced state of the density matrix on a p-body subsystem, represented by a p-RDM, to a target p-body matrix, potentially a p-RDM. The generators of the evolution operators follow the well-known adaptive derivative-assembled pseudo-Trotter method (ADAPT), while the stochastic component is implemented by using a simulated annealing process. The resulting algorithm is independent of any underlying Hamiltonian, and it can be used to decide whether a given p-body matrix is N-representable, establishing a criterion to determine its quality and correcting it. We apply the proposed hybrid ADAPT algorithm to alleged reduced density matrices from a quantum chemistry electronic Hamiltonian, from the reduced Bardeen–Cooper–Schrieffer model with constant pairing, and from the Heisenberg XXZ spin model. In all cases, the proposed method behaves as expected for 1-RDMs and 2-RDMs, evolving the initial matrices toward different targets.

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

Manipulating Growth and Propagation of Correlations in Dipolar Multilayers: From Pair Production to Bosonic Kitaev Models

Here, we study the nonequilibrium dynamics of dipoles confined in multiple stacked two-dimensional layers realizing a long-range interacting quantum spin 1/2 XXX model. We demonstrate that strong in-plane interactions can protect a manifold of collective layer dynamics. This then allows us to map the many-body spin dynamics to bosonic models. In a bilayer configuration we show how to engineer the paradigmatic two-mode squeezing Hamiltonian known from quantum optics, resulting in exponential production of entangled pairs and generation of metrologically useful entanglement from initially prepared product states. In multilayer configurations we engineer a bosonic variant of the Kitaev model displaying chiral propagation along the layer direction. Our study illustrates how the control over interactions, lattice geometry, and state preparation in interacting dipolar systems uniquely afforded by AMO platforms such as Rydberg and magnetic atoms, polar molecules, or trapped ions allows for the control over the temporal and spatial propagation of correlations for applications in quantum sensing and quantum simulation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Stochastic exciton-scattering theory of optical line shapes: Renormalized many-body contributions

Spectral line shapes provide a window into the local environment coupled to a quantum transition in the condensed phase. In this paper, we build upon a stochastic model to account for non-stationary background processes produced by broad-band pulsed laser stimulation, as distinguished from those for stationary phonon bath. In particular, we consider the contribution of pair-fluctuations arising from the full bosonic many-body Hamiltonian within a mean-field approximation, treating the coupling to the system as a stochastic noise term. Herein, using the Itô transformation, we consider two limiting cases for our model, which lead to a connection between the observed spectral fluctuations and the spectral density of the environment. In the first case, we consider a Brownian environment and show that this produces spectral dynamics that relax to form dressed excitonic states and recover an Anderson–Kubo-like form for the spectral correlations. In the second case, we assume that the spectrum is Anderson–Kubo like and invert to determine the corresponding background. Using the Jensen inequality, we obtain an upper limit for the spectral density for the background. The results presented here provide the technical tools for applying the stochastic model to a broad range of problems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Quantum simulations for strong-field QED

Quantum field theory in the presence of strong background fields contains interesting problems where quantum computers may someday provide a valuable computational resource. In the noisy intermediate-scale quantum era it is useful to consider simpler benchmark problems in order to develop feasible approaches, identify critical limitations of current hardware, and build new simulation tools. Here we perform quantum simulations of strong-field QED (SFQED) in 3 + 1 dimensions, using real-time nonlinear Breit-Wheeler pair production as a prototypical process. The strong-field QED Hamiltonian is derived and truncated in the Furry-Volkov mode expansion, and the interactions relevant for Breit-Wheeler are transformed into a quantum circuit. Quantum simulations of a “null double slit” experiment are found to agree well with classical simulations following the application of various error mitigation strategies, including an asymmetric depolarization algorithm which we develop and adapt to the case of Trotterization with a time-dependent Hamiltonian. We also discuss longer-term goals for the quantum simulation of SFQED. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2024

Coulomb confinement in the Hamiltonian limit

The Gribov-Zwanziger scenario attributes the phenomenon of confinement to the instantaneous interaction term in the QCD Hamiltonian in the Coulomb gauge. For a static quark-antiquark pair, it leads to a potential energy that increases linearly with the distance between them. Lattice studies of the SU(2) Yang-Mills theory determined the corresponding (Coulomb) string tension for sources in the fundamental representation, 𝜎 𝐶 , to be about 3 times larger than the Wilson loop string tension, 𝜎 𝐹 . It is far above the Zwanziger variational bound, 𝜎 𝐶 ≥ 𝜎 𝐹 . We argue that the value often reported in the literature is artificially inflated. We examine the lattice definition of the instantaneous potential, find the source of the string tension’s enhancement, and perform its improved determination in SU(2) lattice gauge theory. We report our conservative estimate for the value of the Coulomb string tension as 𝜎 𝐶 /𝜎 𝐹 = 2.0 ± 0.4 and discuss its phenomenological implications.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Coupling of Nondegenerate Topological Modes in Nitrogen Core-Doped Graphene Nanoribbons

Nitrogen core-doping of graphene nanoribbons (GNRs) allows trigonal planar carbon atoms along the backbone of GNRs to be substituted by higher-valency nitrogen atoms. The excess valence electrons are injected into the π-orbital system of the GNR, thereby changing not only its electronic occupation but also its topological properties. We have observed this topological change by synthesizing dilute nitrogen core-doped armchair GNRs with a width of five atoms (N 2 -5-AGNRs). The incorporation of pairs of trigonal planar nitrogen atoms results in the emergence of topological boundary states at the interface between doped and undoped segments of the GNR. These topological boundary states are offset in energy by approximately ΔE = 300 meV relative to the topological end states at the termini of finite 5-AGNRs. Scanning tunneling microscopy (STM) and spectroscopy (STS) reveal that for finite GNRs the two types of topological states can interact through a linear combination of orbitals, resulting in a pair of asymmetric hybridized states. This behavior is captured by an effective Hamiltonian of nondegenerate diatomic molecules, where the analogous interatomic hybridization interaction strength is tuned by the distance between GNR topological modes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗