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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

MOOSE framework enhancements for meshing reactor geometries

MOOSE is an open-source, parallel finite element framework designed to permit rapid development of robust multi-physics modeling capabilities. Under the DOE-NEAMS program, numerous solvers have been developed utilizing the open-source MOOSE framework for multiphysics reactor analysis. These solvers require input finite element meshes representing the discretized geometry. Typically, reactor analysts turn to licensed external tools for creation of reactor geometry meshes. Recently, enhancements have been added to the MOOSE framework to mesh common reactor geometries and improve MOOSE-based application user workflows. Support for hexagonal pins, assemblies, and cores has been added, and Cartesian support has been extended. Options for modeling static and rotating control drums within a hexagonal assembly are now available. Pin, assembly, and plane regions can be identified through automatically applied tags on the mesh called 'reporting IDs' for easier post- processing of physics results. An external open-source triangle routine has been leveraged within MOOSE to mesh core periphery zones. A set of reactor geometry builder routines further streamline the construction of hexagonal and Cartesian cores and include the ability to assign materials to regions during mesh generation. The new meshing routines are available through the MOOSE framework in the open-source 'Reactor' module, and the resulting directly within MOOSE-based applications or exported as Exodus II files for use in other finite element solvers. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

The FastrSHWFS Project Development Motivation, Analysis, & Test Results

The recent 2020 Decadal Survey of Astronomy and Astrophysics listed habitable exoplanet imaging with future extreme adaptive optics (AO) on 30m-class telescopes as a key priority in the coming decade. However, there is a current 100x contrast gap between the best systems today and what is needed to enable this goal. Astronomical AO is a required approach to enable ground-based diffraction-limited imaging of exoplanets on future extremely large telescopes. Time lag between the end of an exposure and the application of deformable mirror commands is a major contributor to the error budget in many AO systems, and detector read time is often a large component of this lag. We present two designs for a modified Shack Hartmann wavefront sensor (SHWFS), named Focal plane Actualized Shifted Technique Realized for a SHWFS (fastrSHWFS), to reduce the time lag component. This design steers the spot pattern at the focal plane into a rectangular or linear array with a custom aspect ratio, reducing readout time. The mask with focus yields aberrated results while the mask with tip/tilt only yields some defined spots. This essay outlines the current SHWFS concept, our fastrSHWFS theoretical solution to addressing time lag, reflection and quality analysis of printed mask designs, and results from testing both masks on the High Contrast Testbed at Lawrence Livermore National Lab. This work follows the test of a previous fastrSHWFS design.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Tuning piezoelectric properties through epitaxy of La 2 Ti 2 O 7 and related thin films

Current piezoelectric sensors and actuators are limited to operating temperatures less than ~200ºC due to the low Curie temperature of the piezoelectric material. The strengthening the piezoelectric coupling of high-temperature piezoelectric materials, such as La 2 Ti 2 O 7 (LTO), would allow sensors to operate across a broad temperature range. The crystalline orientation and piezoelectric coupling direction of LTO thin films can be controlled by epitaxial matching to SrTiO 3 (001), SrTiO 3 (110), and rutile TiO 2 (110) substrates via pulsed laser deposition. The structure and phase purity of the films are investigated by x-ray diffraction and scanning transmission electron microscopy. Piezoresponse force microscopy is used to measure the in-plane and out-of-plane piezoelectric coupling in the films. The strength of the out-of-plane piezoelectric coupling can be increased when the piezoelectric direction is rotated partially out-of-plane via epitaxy. The strongest out-of-plane coupling is observed for LTO/STO(001). Deposition on TiO 2 (110) results in epitaxial La 2/3 TiO 3 , an orthorhombic perovskite of interest as a microwave dielectric material and an ion conductor. La 2/3 TiO 3 can be difficult to stabilize in bulk form, and epitaxial stabilization on TiO 2 (110) is a promising route to realize La 2/3 TiO 3 for both fundamental studies and device applications. Overall, these results confirm that control of the crystalline orientation of epitaxial LTO-based materials can govern the resulting functional properties.

36 MATERIALS SCIENCE↗
DOE OSTI2018

L1 0 -FeNi films on Au-Cu-Ni buffer-layer: a high-throughput combinatorial study

Here, the fct L1 0 -FeNi alloy is a promising candidate for the development of high performance critical-elements-free magnetic materials. Among the different materials, the Au-Cu-Ni alloy has resulted very promising; however, a detailed investigation of the effect of the buffer-layer composition on the formation of the hard FeNi phase is still missing. To accelerate the search of the best Au-Cu-Ni composition, a combinatorial approach based on High-Throughput (HT) experimental methods has been exploited in this paper. HT magnetic characterization methods revealed the presence of a hard magnetic phase with an out-of-plane easy-axis, whose coercivity increases from 0.49 kOe up to 1.30 kOe as the Au content of the Cu-Au-Ni buffer-layer decreases. Similarly, the out-of-plane magneto-crystalline anisotropy energy density increases from 0.12 to 0.35 MJ/m 3 . This anisotropy is attributed to the partial formation of the L1 0 FeNi phase induced by the buffer-layer. In the range of compositions we investigated, the buffer-layer structure does not change significantly and the modulation of the magnetic properties with the Au content in the combinatorial layer is mainly related to the different nature and extent of interlayer diffusion processes, which have a great impact on the formation and order degree of the L1 0 FeNi phase.

25 ENERGY STORAGE↗
DOE OSTI2014

SU-E-J-92: On-Line Cone Beam CT Based Planning for Emergency and Palliative Radiation Therapy

Purpose: To evaluate and develop the feasibility of on-line cone beam CT based planning for emergency and palliative radiotherapy treatments. Methods: Subsequent to phantom studies, a case library of 28 clinical megavoltage cone beam CT (MVCBCT) was built to assess dose-planning accuracies on MVCBCT for all anatomical sites. A simple emergency treatment plan was created on the MVCBCT and copied to its reference CT. The agreement between the dose distributions of each image pair was evaluated by the mean dose difference of the dose volume and the gamma index of the central 2D axial plane. An array of popular urgent and palliative cases was also evaluated for imaging component clearance and field-of-view. Results: The treatment cases were categorized into four groups (head and neck, thorax/spine, pelvis and extremities). Dose distributions for head and neck treatments were predicted accurately in all cases with a gamma index of >95% for 2% and 2 mm criteria. Thoracic spine treatments had a gamma index as low as 60% indicating a need for better uniformity correction and tissue density calibration. Small anatomy changes between CT and MVCBCT could contribute to local errors. Pelvis and sacral spine treatment cases had a gamma index between 90% and 98% for 3%/3 mm criteria. The limited FOV became an issue for large pelvis patients. Imaging clearance was difficult for cases where the tumor was positioned far off midline. Conclusion: The MVCBCT based dose planning and delivery approach is feasible in many treatment cases. Dose distributions for head and neck patients are unrestrictedly predictable. Some FOV restrictions apply to other treatment sites. Lung tissue is most challenging for accurate dose calculations given the current imaging filters and corrections. Additional clinical cases for extremities need to be included in the study to assess the full range of site-specific planning accuracies. This work is supported by Siemens.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Phase-field modeling of stacking structure formation and transition of δ-hydride precipitates in zirconium

d-hydride structures in Zr nuclear fuel-rod cladding significantly affect mechanical properties. In this work, a micromechanical phase-field model is developed to investigate the effect of interfacial energy anisotropy and elastic interaction on the nucleation, stacking structure formation, and stacking structure transition of d-hydride precipitates. It is found that the nucleation probability and growth of d-hydride near pre-existing hydrides are strongly spatially dependent. Results show that (1) the d-hydride precipitate has a platelet-like shape. The large shear deformation associated with lattice mismatches and a small interfacial energy of its broad interface cause the orientation of the plate-like d-hydride off the basal plane a small angle of approximately 14.7°. (2) Stress-induced nucleation of d-hydride precipitates near a pre-existing hydride results in the unique stacking structure formation of d-hydride precipitates. (3) The morphology and alignment of hydride stacking structures, called as macroscopic hydrides which consist of microscopic hydrides with certain stacking sequences, change under stresses. The alignment of macroscopic hydrides changes from along the circumferential direction to along the radial direction under tensile hoop stress while the orientation of microscopic hydrides remains parallel to the basal plane. These results are in agreement with experimental observations. The simulations reveal that stress-induced heterogeneous nucleation and growth is the mechanism for the formation and transition of unique macro-hydride stacking structures observed in in Zr nuclear fuel-rod cladding.

Han, G. M.↗
DOE OSTI2024

High-performance 2D electronic devices enabled by strong and tough two-dimensional polymer with ultra-low dielectric constant

As the feature size of microelectronic circuits is scaling down to nanometer order, the increasing interconnect crosstalk, resistance-capacitance (RC) delay and power consumption can limit the chip performance and reliability. To address these challenges, new low-k dielectric (k < 2) materials need to be developed to replace current silicon dioxide (k = 3.9) or SiCOH, etc. However, existing low-k dielectric materials, such as organosilicate glass or polymeric dielectrics, suffer from poor thermal and mechanical properties. Two-dimensional polymers (2DPs) are considered promising low-k dielectric materials because of their good thermal and mechanical properties, high porosity and designability. Here, we report a chemical-vapor-deposition (CVD) method for growing fluoride rich 2DP-F films on arbitrary substrates. We show that the grown 2DP-F thin films exhibit ultra-low dielectric constant (in plane k = 1.85 and out-of-plane k = 1.82) and remarkable mechanical properties (Young’s modulus > 15 GPa). We also demonstrated the improved performance of monolayer MoS 2 field-effect-transistors when utilizing 2DP-F thin films as dielectric substrates.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Non-covalent planarizing interactions yield highly ordered and thermotropic liquid crystalline conjugated polymers

Controlling the multi-level assembly and morphological properties of conjugated polymers through structural manipulation has contributed significantly to the advancement of organic electronics. In this work, a redox active conjugated polymer, TPT–TT, composed of alternating 1,4-(2-thienyl)-2,5-dialkoxyphenylene (TPT) and thienothiophene (TT) units is reported with non-covalent intramolecular S⋯O and S⋯H–C interactions that induce controlled main-chain planarity and solid-state order. As confirmed by density functional theory (DFT) calculations, these intramolecular interactions influence the main chain conformation, promoting backbone planarization, while still allowing dihedral rotations at higher kinetic energies (higher temperature), and give rise to temperature-dependent aggregation properties. Thermotropic liquid crystalline (LC) behavior is confirmed by cross-polarized optical microscopy (CPOM) and closely correlated with multiple thermal transitions observed by differential scanning calorimetry (DSC). This LC behavior allows us to develop and utilize a thermal annealing treatment that results in thin films with notable long-range order, as shown by grazing-incidence X-ray diffraction (GIXD). Specifically, we identified a first LC phase, ranging from 218 °C to 107 °C, as a nematic phase featuring preferential face-on π–π stacking and edge-on lamellar stacking exhibiting a large extent of disorder and broad orientation distribution. A second LC phase is observed from 107 °C to 48 °C, as a smectic A phase featuring sharp, highly ordered out-of-plane lamellar stacking features and sharp tilted backbone stacking peaks, while the structure of a third LC phase with a transition at 48 °C remains unclear, but resembles that of the solid state at ambient temperature. Furthermore, the significance of thermal annealing is evident in the ∼3-fold enhancement of the electrical conductivity of ferric tosylate-doped annealed films reaching 55 S cm −1 . More importantly, thermally annealed TPT–TT films exhibit both a narrow distribution of charge-carrier mobilities (1.4 ± 0.1) × 10 −2 cm 2 V −1 s −1 along with a remarkable device yield of 100% in an organic field-effect transistor (OFET) configuration. This molecular design approach to obtain highly ordered conjugated polymers in the solid state affords a deeper understanding of how intramolecular interactions and repeat-unit symmetry impact liquid crystallinity, solution aggregation, solution to solid-state transformation, solid-state morphology, and ultimately device applications.

Chemistry↗
DOE OSTI2015

A magnetic micro-manipulator for application of three dimensional forces

Magnetic manipulation finds diverse applications in actuation, characterization, and manipulation of micro- and nano-scale samples. This paper presents the design and development of a novel magnetic micro-manipulator for application of three-dimensional forces on a magnetic micro-bead. A simple analytical model is proposed to obtain the forces of interaction between the magnetic micro-manipulator and a magnetic micro-bead. Subsequently, guidelines are proposed to perform systematic design and analysis of the micro-manipulator. The designed micro-manipulator is fabricated and evaluated. The manipulator is experimentally demonstrated to possess an electrical bandwidth of about 1 MHz. The ability of the micro-manipulator to apply both in-plane and out-of-plane forces is demonstrated by actuating permanent-magnet micro-beads attached to micro-cantilever beams. The deformations of the micro-cantilevers are also employed to calibrate the dependence of in-plane and out-of-plane forces on the position of the micro-bead relative to the micro-manipulator. The experimentally obtained dependences are found to agree well with theory.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2019

Finding the “lost-time” in detonator function

Exploding bridgewire (EBW) detonators were invented during the Manhattan Project over 75 years ago. Initially developed for precise timing and reproducibility, they continue to be used in many applications. Despite widespread use and reliability, their mechanism for function remains controversial. They provide precision timing, yet their function is described in terms of a “lost time” accounting for nearly half of the function time. Buried in understanding the EBW function is the mystery of how an incoherent impulse such as powering a bridgewire yields the coherent energy output of a detonation. Even the general phenomena by which release of chemical energy in a crystalline organic explosive becomes associated with the sonic plane of a steady detonation wave remain uncertain. Here, we investigate the EBW function with a suite of diagnostics and show that stationary heating occurs during the “lost-time.” We use x-ray radiography to observe the propagation of a shock wave from bridgewire vaporization and establish that the origin of the radially emanating detonation wave is spatially separated from the initial shock. Utilizing the observed temperature as a boundary condition in our explosive response models yields a thermal ignition consistent with the “lost-time” and detonation location consistent with previous work. With these findings, we define a direct thermal initiation mechanism for the EBW function consistent with previous integral observations and explain the displacement of initiation from the bridgewire burst in time and space.

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

Dislocation half-loop control for optimal V-defect density in GaN-based light emitting diodes

V-defects are morphological defects that typically form on threading dislocations during epitaxial growth of $(0001)$-oriented GaN layers. A V-defect is a hexagonal pyramid-shaped depression with six {$10\bar{1}1$}-oriented sidewalls. These semipolar sidewalls have a lower polarization barrier than the polarization barriers present between the polar c-plane quantum wells and quantum barriers and can laterally inject carriers directly into quantum wells in GaN-based light emitting diodes (LEDs). This is especially important, as the high polarization field in c-plane GaN is a significant factor in the high forward voltage of GaN LEDs. The optimal V-defect density for efficient lateral carrier injection in a GaN LED (∼10 9 cm −2 ) is typically an order of magnitude higher than the threading dislocation density of GaN grown on patterned sapphire substrates (∼10 8 cm −2 ). Pure-edge dislocation loops have been known to exist in GaN, and their formation into large V-defects via low-temperature growth with high Si-doping has recently been studied. Here, in this work, we develop a method for pure-edge threading dislocation half-loop formation and density control via disilane flow, growth temperature, and thickness of the half-loop generation layer. We also develop a method of forming the threading dislocation half-loops into V-defects of comparable size to those originating from substrate threading dislocations.

Crystallographic defects↗
DOE OSTI2015

Investigation of the Effect of In-Plane Fiber Waviness in Composite Materials through Multiple Scales of Testing and Finite Element Modeling

Defects in materials can reduce strengths and lifetimes of manufactured parts. The number of possible defects increases with the complexity inherent in composite materials. The wind industry uses composite wind turbine blades in which the manufacturing process induces a number of defects. In order for the wind industry to continue sustainable expansion, the effects of defects must be better understood. In-plane (IP) fiber waviness is the focus of this work. The three main parts of this work include testing on the coupon level, modeling on the coupon level, and testing of beams in four-point bending (with and without defects). The coupon level testing includes partial IP waves, similar to those in manufactured parts, rather than full width IP waves. This allows investigation into complex interactions and varying failure mechanisms caused by the fiber misalignment gradient. Partial waves are also modeled to both validate testing as well as to increase robustness of a previously developed progressive damage modeling method. Lastly, a sandwich beam test specimen for testing in 4-point bending is developed to investigate the effects of fiber waviness in both tension and compression when loaded in flexure.

36 MATERIALS SCIENCE↗
DOE OSTI2023

AMMT FY23 HFIR Irradiation Test Matrix – Supported by the Design of a Miniature Bend Bar Irradiation Vehicle

With the continued advancement of additive manufacturing (AM) techniques, interest has grown in the development and qualification of steels produced via these methods for use in the structural components of advanced nuclear reactors. Therefore, it is crucial that the properties of these materials such as the tensile strength and fracture toughness be investigated following neutron irradiation to support their use in industry. To that end, a test plan to irradiate several tensile and bend bar specimens in the High Flux Isotope Reactor (HFIR) at Oak Ridge National Laboratory was proposed, along with the development of a new “MINBEN” capsule design that features MBS-1 bend bar specimens that have a larger cross-sectional area than those of previous designs, which allows for higher temperature out-of-pile testing. The specimens include AM 316H stainless steel with wrought 316H and A709 stainless steels for reference, and they will be irradiated at 2 dpa and 10 dpa—corresponding to roughly 1 and 5 cycles at the HFIR midplane—at temperatures of 400°C and 600°C. The MINBEN design was found to be capable of providing specimen test plane average temperatures in the range of 220–660°C for six specimens, with a min-max spread in this temperature of ~40°C and a 95% confidence interval of ~24°C. This analysis shows that the capsule provides an effective vehicle for gathering needed high-temperature fracture toughness data.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Optical Design and Characterization of 40-GHz Detector and Module for the BICEP Array

Families of cosmic inflation models predict a primordial gravitational-wave background that imprints B-mode polarization pattern in the cosmic microwave background (CMB). High-sensitivity instruments with wide frequency coverage and well-controlled systematic errors are needed to constrain the faint B-mode amplitude. We have developed antenna-coupled transition edge sensor arrays for high-sensitivity polarized CMB observations over a wide range of millimeter-wave bands. BICEP array, the latest phase of the BICEP/Keck experiment series, is a multi-receiver experiment designed to search for inflationary B-mode polarization to a precision σ(r) between 0.002 and 0.004 after 3 full years of observations, depending on foreground complexity and the degree of lensing removal. We describe the electromagnetic design and measured performance of BICEP array’s low-frequency 40-GHz detector, their packaging in focal plane modules, and optical characterization including efficiency and beam matching between polarization pairs. We summarize the design and simulated optical performance, including an approach to improve the optical efficiency due to mismatch losses. Here, we report the measured beam maps for a new broadband corrugation design to minimize beam differential ellipticity between polarization pairs caused by interactions with the module housing frame, which helps minimize polarized beam mismatch that converts CMB temperature to polarization (T→P) anisotropy in CMB maps.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Enhanced Thermal Conductivity in a Diamine-Appended Metal-Organic Framework as a Result of Cooperative CO 2 Adsorption

Using diamine-appended variants of the metal-organic framework M 2 (dobpdc) (M = Mg, Mn, Fe, Co, Zn; dobpdc 4- = 4,4'-dioxidobiphenyl-3,3'-dicarboxylate) exhibit exceptional CO 2 capture properties owing to a unique cooperative adsorption mechanism, and thus hold promise for use in the development of energy- and cost-efficient CO 2 separations. Understanding the nature of thermal transport in these materials is essential for such practical applications, however, as temperature rises resulting from exothermic CO 2 uptake could potentially offset the energy savings offered by such cooperative adsorbents. Here, molecular dynamics (MD) simulations are employed in investigating thermal transport in bare and e-2-appended Zn 2 (dobpdc) (e-2 = N -ethylethylenediamine), both with and without CO 2 as a guest. In the absence of CO 2 , the appended diamines function to enhance thermal conductivity in the ab -plane of e-2-Zn 2 (dobpdc) relative to the bare framework, as a result of noncovalent interactions between adjacent diamines that provide additional heat transfer pathways across the pore channel. Upon introduction of CO 2 , the thermal conductivity along the pore channel (the c -axis) increases due to the cooperative formation of metal-bound ammonium carbamates, which serve to create additional heat transfer pathways. In contrast, the thermal conductivity of the bare framework remains unchanged in the presence of zinc-bound CO 2 but decreases in the presence of additional adsorbed CO 2 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Discovery of hard-magnetic domains in two-dimensional arrays of soft-magnetic Fe{sub 3}O{sub 4} nanocubes

In this study, abnormal hard-magnetic domains were discovered in Fe{sub 3}O{sub 4}@C composite material, in which well-ordered 16-nm-sized Fe{sub 3}O{sub 4} cubes were tightly embedded into carbon sheets of tens of nanometers thick. It was found that ca. 40 columns of Fe{sub 3}O{sub 4} nanocubes magnetically self-assembled into a single strip-type domain with perpendicular magnetic anisotropy. More strikingly, remarkable domain misalignments, which were very similar to common edge dislocations among atomic planes in crystal lattices, were clearly observed and termed as “domain dislocation” in this work. The hard-magnetic properties of Fe{sub 3}O{sub 4}@C material, including large coercivity of 2150 Oe, high M{sub R}/M{sub S} value of 0.9, and strong anisotropy energy of 3.772 × 10{sup 5} erg/cm{sup 3}, were further ascertained by carefully designed electromagnetic absorption contrast experiments. It is anticipated that the discovery of hard-magnetic domains and domain dislocations within 2-D arrays of soft-magnetic nanomaterials will shed new light on the development of high-density perpendicular magnetic recording industry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Estimating perturbed stress from 3-D borehole displacements induced by fluid injection in fractured or faulted shales

SUMMARY Hydrofracturing stress measurements in fractured and anisotropic shales are notoriously difficult, because opening of existing geological features tends to prevent the creation of a pure hydraulic fracture perpendicular to the least compressive principal stress. Here we show how adding 3-D borehole-displacement measurements while conducting the hydraulic injection test helps to better constrain the principal stress orientations and magnitudes. We developed a 3-D fully coupled hydromechanical numerical model to analyse the displacement, fluid pressure and injection flow-rate data measured during an injection pressure-step-rate test conducted to activate a faulted borehole interval in the Mont Terri Opalinus Clay (Switzerland). We find that injected fluids can only penetrate the fault when it is at or above the Coulomb failure pressure. Borehole displacement orientations are sensitive to a ∼15° variation in the stress–tensor orientation and a 1 MPa stress magnitude variation. Although some dispersion occurs while rupture is propagating along the fault plane ∼4 m away from the borehole, the maximum density of displacement orientations consistently informs about the stress orientation. Thus, an extended injection step-rate approach coupled with an accurate in situ measurement of the borehole wall displacements can be used to better constrain the local stress field perturbations in fractured shales and in heterogeneous rock in general.

Guglielmi, Yves↗
DOE OSTI2021

Theory of Trotter Error with Commutator Scaling

The Lie-Trotter formula, together with its higher-order generalizations, provides a simple approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly understood. We develop a theory of Trotter error that overcomes the limitations of truncating the Baker-Campbell-Hausdorff expansion. Our analysis directly exploits the commutativity of operator summands, producing tighter error bounds for both real- and imaginary-time evolutions. Whereas previous work achieves similar goals for systems with geometric locality or Lie-algebraic structure, our approach holds in general. We give a host of improved algorithms for digital quantum simulation and quantum Monte Carlo methods, nearly matching or even outperforming the best previous results. Our applications include: (i) a simulation of second-quantized plane-wave electronic structure, nearly matching the interaction-picture algorithm of Low and Wiebe; (ii) a simulation of $k$-local Hamiltonians almost with induced one-norm scaling, faster than the qubitization algorithm of Low and Chuang; (iii) a simulation of rapidly decaying power-law interactions, outperforming the Lieb-Robinson-based approach of Tran et al.; (iv) a hybrid simulation of clustered Hamiltonians, dramatically improving the result of Peng, Harrow, Ozols, and Wu; and (v) quantum Monte Carlo simulations of the transverse field Ising model and quantum ferromagnets, tightening previous analyses of Bravyi and Gosset. We obtain further speedups using the fact that product formulas can preserve the locality of the simulated system. Specifically, we show that local observables can be simulated with complexity independent of the system size for power-law interacting systems, which implies a Lieb-Robinson bound nearly matching a recent result of Tran et al. Our analysis reproduces known tight bounds for first- and second-order formulas. We further investigate the tightness of our bounds for higher-order formulas. For quantum simulation of a one-dimensional Heisenberg model with an even-odd ordering of terms, our result overestimates the complexity by only a factor of $5$. Our bound is also close to tight for power-law interactions and other orderings of terms. This suggests that our theory can accurately characterize Trotter error in terms of both the asymptotic scaling and the constant prefactor.

quantum computing, numerical analysis↗