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At least 1,261 records · Page 70

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DOE OSTI2022

Structural stability of thin overhanging walls during material extrusion additive manufacturing of thermoset-based ink

Recent developments have enabled material extrusion additive manufacturing of thermoset-based composite inks on the large scale. In addition, printing out-of-plane components is of broad interest to the polymer material extrusion community. Here, we address some of the challenges associated with both large-scale and out-of-plane thermoset material extrusion additive manufacturing by studying the height at which thin overhanging walls collapse. Walls at a range of overhang angles were printed until they collapsed. An optical camera captured the profile of each wall throughout the print, allowing the collapse height to be identified and the geometric fidelity to the programmed angle to be evaluated. Using previously measured rheological properties, predictive models were generated to approximate the collapse height and profile of the deflected walls. First, an analytical model was created to predict the height at which the walls would yield. The analytical model assumes the walls exhibit a perfectly linear profile; however, experiments proved this assumption to be false. Therefore, a finite element simulation was developed to account for the elastic deflection that occurs during printing. The finite element simulation predicts both the yield height and the deflected profile after the deposition of each layer. For the properties of the thermoset ink used here, the yield height predicted by the analytical model and finite element simulation are virtually identical. These predictions match experimental data reasonably well, but minor errors are observed. Accounting for the fully plastic moment appears to explain the small mismatch between experimental data and predictions. Additionally, the finite element simulation provides an excellent prediction of the deflected profile before the wall begins to collapse. Finally, by demonstrating that the collapse height and deflected profile of thin overhanging walls can be predicted, this work illustrates how the soft viscoelastic properties of thermoset-based composite inks limit the scale of a key feature required to print some nonplanar components. It also provides a basis to tailor in-process curing systems to suppress deflection and collapse of thin overhanging walls.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Schmid factor crack propagation and tracking crystallographic texture markers of microstructural condition in direct energy deposition additive manufacturing of Ti-6Al-4V

Metallic additive manufacturing (AM) provides a customizable and tailorable manufacturing process for new engineering designs and technologies. The greatest challenge currently facing metallic AM is maintaining control of microstructural evolution during solidification and any solid state phase transformations during the build process. Ti-6Al-4V has been extensively surveyed in this regard, with the potential solid state and solidification microstructures explored at length. In this study, we evaluate the applicability of previously determined crystallo- graphic markers of microstructural condition observed in electron beam melting powder bed fusion (PBF-EB) builds of Ti-6Al-4V in a directed energy deposition (DED) build process. The aim of this effort is to elucidate whether or not these specific crystallographic textures are useful tools for indicating microstructural conditions in AM variants beyond PBF-EB. Parent β-Ti grain size was determined to be directly related to α-Ti textures in the DED build process, and the solid state microstructural condition could be inferred from the intensity of specific α-Ti orientations. Qualitative trends on the as-solidified β-Ti grain size were also determined to be related to the presence of a fiber texture, and proposed as a marker for as-solidified grain size in any cubic metal melted by AM. Analysis of the DED Ti-6Al-4V build also demonstrated a near complete fracture of the build volume, suspected to originate from accumulated thermal stresses in the solid state. Crack propagation was found to only appreciably occur in regions of slow cooling with large α +β colonies. Schmid factors for the basal and prismatic α-Ti systems explained the observed crack pathway, including slower bifurcation in colonies with lower Schmid factors of both slip systems. Colony morphologies and localized equiaxed β-Ti solidification were also found to originate from build pauses during production and uneven heating of the build edges during deposition. Tailoring of DED Ti-6Al-4V microstructures with the insight gained here is proposed, along with cautionary insight on preventing unplanned build pauses to maintain an informed and controlled thermal environment for microstructural control.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Observation of spatter-induced stochastic lack-of-fusion in laser powder bed fusion using in situ process monitoring

Material produced via additive manufacturing (AM) continues to exhibit variable mechanical properties despite apparent optimization of processing parameters, inhibiting qualification efforts and limiting use in critical applications. Stochastic lack-of-fusion flaws may help explain this variability, but the origin of these seemingly random defects has to this point remained unclear. In this work, we show that spatter particles, material ejected from the laser melt pool, are directly responsible for generating stochastic lack-of-fusion in laser-based powder bed fusion components through the application of spatial statistics. Herein a statistically significant, causal relationship between spatter particles and stochastic lack-of-fusion is established, and the spatial and morphological relationships between spatter and internal flaws are investigated. The occurrence of spatter-induced lack-of-fusion in relation to the inert gas flow and laser trajectory direction is also investigated, and recommendations for mitigating the occurrence of spatter are evaluated.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Effects of size, geometry, and testing temperature on additively manufactured Ti-6Al-4V titanium alloy

This article presents a comprehensive study concerning size and geometry effect on the ambient and high-temperature mechanical behavior of additively manufactured laser powder bed fusion Ti-6Al-4V alloy. Key mechanical property metrics are presented, including strain hardening rate, yield strength, and Young’s modulus as a function of thickness and testing temperature (ambient, 250 °C, and 450 °C). Here, the effect of specimen size on manufacturing-induced microstructural feature formation is demonstrated and discussed. A detailed analysis regarding Young’s modulus, yield strength, and strain hardening rate variation at elevated temperatures is also presented. Size effect and temperature-sensitive deformation mechanisms are linked to the underlying microstructural deformation mechanisms activated at respective temperatures. Counter-intuitively, this study determined that irrespective of the geometry, strain hardening rates increased as temperature increased. An in-depth microstructural examination is presented to explain the stated observation. The texture of Interrupted tensile test samples examined for ambient, 250 °C, and 450 °C post-yield was observed to be unchanged, indicating the strain hardening behavior was not texture dependent. Schmid factor analysis, coupled with experimental findings from previous work, was implemented to generate a hypothesis. This hypothesis suggests that the drop in critical resolved shear stress for basal and pyramidal slip systems, as temperature increases, paired with the high dislocation density of laser powder bed fusion Ti-6Al-4V, leads to dislocation entanglement and results in increased strain hardening at elevated temperatures.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Understanding the influence of boron in additively manufactured GammaPrint®-700 CoNi-based superalloy

Boron is commonly added to superalloys in small amounts to enhance creep resistance, but can lead to cracking at high concentrations, especially during the additive manufacturing process. Two variants of CoNi-based GammaPrint®-700 superalloy with different B contents (0.08 at% vs 0.16 at%) were printed via laser powder bed fusion (LPBF) with the same printing parameters, with only the high B alloy exhibiting solidification cracking. Atom probe tomography (APT) revealed stronger segregation behaviors in the high B alloy compared to the low B alloy at both the inter-dendritic regions and grain boundaries (GBs). The segregation behavior at inter-dendritic regions was well captured with Scheil simulation and can correlate with the existing cracking susceptibility index (CSI) on cracking tendencies, although high angle GBs are where cracking occurs according to electron backscatter diffraction (EBSD) measurements. Additionally, the extent of GB segregation was compared between the high B and low B alloy. Higher B additions led to significantly more GB B segregation in the high B alloy compared to the low B alloy. Further, for the high B alloy, the cracked region of one GB exhibited higher levels of B compared to the uncracked region of the same GB. However, much higher B contents were also found in two other uncracked GBs in the high B alloy, which demonstrates that higher GB B concentrations are not fully responsible for the cracking. A much larger variance in GB B segregation content was found in the high B alloy compared to the low B alloy. These phenomena were explained with a solidification model with the GB segregation content expressed explicitly by a modified Langmuir-McLean equation. This model linked the GB segregation content with solidification undercooling, which can be used as quantitative cracking criteria for future builds.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Dissolution zone model of the oxide structure in additively manufactured dispersion-strengthened alloys

The structural evolution of oxides in dispersion-strengthened superalloys during laser-powder bed fusion is considered in detail. Alloy chemistry and process parameter effects on oxide structure are assessed through a parameter study on the model alloy Ni-20Cr, doped with varying concentrations of Y 2 O 3 and Al. Small angle neutron scattering measurements of the dispersoid size distribution show the dispersoid size increases with higher laser power, slower scan speed, and increasing Y 2 O 3 and Al content. Complementary electron microscopy measurements reveal reactions between Y 2 O 3 and Al, even in nanoscale dispersoids, and the presence of micron-scale oxide slag inclusions in select specimens. A scaling analysis of mass and momentum transport within the melt pool, presented here, establishes that diffusional structural evolution mechanisms dominate for nanoscale dispersoids, while fluid forces and advection become significant for larger slag inclusions. These findings are developed into a theory of dispersoid structural evolution, integrating quantitative models of diffusional processes – dispersoid dissolution, nucleation, growth, coarsening – with a reduced order model of time-temperature trajectories of fluid parcels within the melt pool. Calculations of the dispersoid size in single-pass melting reveal a zone in the center of the melt track in which the oxide feedstock fully dissolves. Within this zone the final Y 2 O 3 size is independent of feedstock size and determined by nucleation and growth kinetics. If the dissolution zones of adjacent melt tracks overlap sufficiently with each other to dissolve large oxides, formed during printing or present in the powder feedstock, then the dispersoid structure throughout the build volume is homogeneous and matches that from a single pass within the dissolution zone. Gaps between adjacent dissolution zones result in oxide accumulation into larger slag inclusions. Predictions of final dispersoid size and slag formation using this dissolution zone model match the present experimental data and explain process-structure linkages speculated in the open literature.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Recent land cover changes in the Southwestern US lead to an increase in surface temperature

The increase in large-scale land cover change (LCC) in recent decades, particularly in response to climate-driven disturbances, has potential to impact local and regional changes in climate due to modification of carbon sources and sinks, albedo, surface roughness and energy fluxes. Using observational data, we predict the impact of two of the most extensive LCCs occurring in the Southwestern US: drought-induced tree mortality and shrub encroachment into grasslands, on surface temperature. We developed a new energy balance method that extracts the biophysical responses to environmental conditions, to predict how structural changes in albedo, surface roughness and canopy conductance following LCC will alter surface temperature. This method allows us not only to explain the observed differences in surface temperature between two non-adjacent study sites with different environmental conditions, but also to separate the contribution of biophysical and non-biophysical properties to surface temperature. Our results suggest that changes in biophysical properties due to shrub encroachment and tree mortality in the Southwestern US (independent of changes in other environmental properties) can potentially lead to an increase in midday surface temperature (11AM to 2PM) of 1 to 2 degrees Celsius, comparable to changes in surface temperature following deforestation. Although the average surface temperature increase in response to both shrub encroachment and tree mortality is similar, the biophysical properties driving the temperature change are different in each scenario. Change in aerodynamic conductance following tree mortality is the largest contributor to heating, while reduced albedo and canopy conductance drive the increase in surface temperature following shrub encroachment. Finally, we also show how this increase in daytime surface temperature could be further intensified with future climate, especially with the expected reduction in soil water availability in the Southwest.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Environment-sensitivity functions for gross primary productivity in light use efficiency models

The sensitivity of photosynthesis to environmental changes is essential for understanding carbon cycle responses to global climate change and for the development of modeling approaches that explains its spatial and temporal variability. We collected a large variety of published sensitivity functions of gross primary productivity (GPP) to different forcing variables to assess the response of GPP to environmental factors. These include the responses of GPP to temperature; vapor pressure deficit, some of which include the response to atmospheric CO 2 concentrations; soil water availability (W); light intensity; and cloudiness. These functions were combined in a full factorial light use efficiency (LUE) model structure, leading to a collection of 5600 distinct LUE models. Each model was optimized against daily GPP and evapotranspiration fluxes from 196 FLUXNET sites and ranked across sites based on a bootstrap approach. The GPP sensitivity to each environmental factor, including CO 2 fertilization, was shown to be significant, and that none of the previously published model structures performed as well as the best model selected. From daily and weekly to monthly scales, the best model's median Nash-Sutcliffe model efficiency across sites was 0.73, 0.79 and 0.82, respectively, but poorer at annual scales (0.23), emphasizing the common limitation of current models in describing the interannual variability of GPP. Although the best global model did not match the local best model at each site, the selection was robust across ecosystem types. The contribution of light saturation and cloudiness to GPP was observed across all biomes (from 23% to 43%). Temperature and W dominates GPP and LUE but responses of GPP to temperature and W are lagged in cold and arid ecosystems, respectively. The findings of this study provide a foundation towards more robust LUE-based estimates of global GPP and may provide a benchmark for other empirical GPP products.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Dryness controls temperature-optimized gross primary productivity across vegetation types

Temperature response of gross primary productivity (GPP) is a well-known property of ecosystem, but GPP at the optimum temperature (GPP_T opt ) has not been fully discussed. Our understanding of how GPP_T opt responds to warming and water availability is highly limited. Here, in this study, we analyzed data at 326 globally distributed eddy covariance sites (79°N-37°S), to identify controlling factors of GPP_T opt . Although GPP_T opt was significantly influenced by soil moisture, global solar radiation, mean annual temperature, and vapor pressure deficit in a non-linear pattern (R 2 = 0.47), the direction and magnitude of these climate variables’ effects on GPP_T opt depend on the dryness index (DI), a ratio of potential evapotranspiration to precipitation. The spatial pattern showed that soil moisture did not affect GPP_T opt across energy-limited sites with DI < 1 while dominated GPP_T opt across water-limited sites with DI >1. The temporal pattern showed that GPP_T opt was lowered by warming or low precipitation in water-limited sites while energy-limited sites tended to maintain a stable GPP_T opt regardless of changes in air temperature. Vegetation types in humid climates tended to have higher GPP_T opt and were more likely to benefit from a warmer climate since it was not restricted by water conditions. This study highlights that the response of GPP_T opt to global warming depends on the dryness conditions, which explains the nonlinear control of water and temperature over GPP_T opt . Our finding is essential to realistic prediction of terrestrial carbon uptake under future climate and vegetation conditions.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Causality guided machine learning model on wetland CH 4 emissions across global wetlands

Wetland CH 4 emissions are among the most uncertain components of the global CH 4 budget. The complex nature of wetland CH 4 processes makes it challenging to identify causal relationships for improving our understanding and predictability of CH 4 emissions. In this study, we used the flux measurements of CH 4 from eddy covariance towers (30 sites from 4 wetlands types: bog, fen, marsh, and wet tundra) to construct a causality-constrained machine learning (ML) framework to explain the regulative factors and to capture CH 4 emissions at sub-seasonal scale. We found that soil temperature is the dominant factor for CH 4 emissions in all studied wetland types. Ecosystem respiration (CO 2 ) and gross primary productivity exert controls at bog, fen, and marsh sites with lagged responses of days to weeks. Integrating these asynchronous environmental and biological causal relationships in predictive models significantly improved model performance. More importantly, modeled CH 4 emissions differed by up to a factor of 4 under a +1°C warming scenario when causality constraints were considered. These results highlight the significant role of causality in modeling wetland CH 4 emissions especially under future warming conditions, while traditional data-driven ML models may reproduce observations for the wrong reasons. Our proposed causality-guided model could benefit predictive modeling, large-scale upscaling, data gap-filling, and surrogate modeling of wetland CH 4 emissions within earth system land models.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

SIF-based GPP modeling for evergreen forests considering the seasonal variation in maximum photochemical efficiency

Solar-induced chlorophyll fluorescence (SIF) has shown great potential in estimating gross primary production (GPP). However, their quantitative relationship is not invariant, which undermines the reliability of empirical SIF-based GPP estimation at fine spatiotemporal scales, especially under extreme conditions. In this study, we developed a parsimonious mechanistic model for SIF-based GPP estimation in evergreen needle forests (ENF) by employing the Mechanistic Light Response framework and Eco-Evolutionary theory to describe the light and dark reactions during photosynthesis, respectively. Specifically, we found that considering the seasonal variation in a key parameter of the MLR framework, the maximum photochemical efficiency of photosystem II (Φ PSIImax ), can avoid the GPP overestimation in winter and early spring due to the relatively low environmental sensitivity of SIF. Compared to the estimates from other benchmark models, our GPP estimates were closer to the 1: 1 line and had higher accuracy (average R 2 = 0.86, RMSE=1.99 μmol m -2 s -1 ) across sites. Furthermore, the changes in the relationship between SIF and J (refers to the electron transport rate) contribute a lot to the dynamic SIF–GPP relationship in this study, while the J–GPP relationship is less variant when the temperature drops. Further, the seasonal variation in the SIF–J relationship, especially the reduction in its slope at low temperatures, is found largely explained by the Φ PSIImax . These results indicate the importance of the uncertainty caused by the variation in the SIF–J relationship for SIF-based GPP estimation, and the consideration of changes in Φ PSIImax under extreme conditions (such as severe winter in this study) is crucial for the improvement of GPP estimation via SIF.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Hysteresis area at the canopy level during and after a drought event in the Central Amazon

Understanding forest water limitation during droughts within a warming climate is essential for accurate predictions of forest-climate interactions. In hyperdiverse ecosystems like the Amazon forest, the mechanisms shaping hysteresis patterns in transpiration relative to environmental factors are not well understood. From this perspective, we investigated these dynamics by conducting in situ leaf-level measurements throughout and after the 2015 El Niño-Southern Oscillation (ENSO) drought. Our findings indicate a substantial increase in the hysteresis area (H area ) among transpiration (E), vapor pressure deficit (VPD), and stomatal conductance (g s ) at canopy level during the ENSO peak, attributed to both temporal lag and differences in magnitude between g s and VPD peaks. Specifically, the canopy species Pouteria anomala exhibited an increased H area , due to earlier maximum g s rates leading to a greater temporal lag with VPD compared to the post-drought period. Additionally, leaf water potential (ψ L ) and canopy temperature (T canopy ) showed larger H area during the ENSO peak compared to post-drought conditions across all studied species, suggesting that stomatal closure, particularly during the afternoon, acts to minimize water loss and may explain the counterclockwise hysteresis observed between ψ L and T canopy . Here, the pronounced H area during the drought points to a potential imbalance between water supply and demand, underlining the role of stomatal behavior of isohydric species in response to drought.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Refining water and carbon fluxes modeling in terrestrial ecosystems via plant hydraulics integration

Plant hydraulics substantially affects terrestrial water and carbon cycles by modulating water transport and carbon assimilation. Despite improved drought simulations in certain ecosystems through their integration into land surface models (LSMs), the broader application of plant hydraulics in diverse ecosystems and hydroclimates is still underexplored. Here, in this study, we implemented the recently developed Noah-Multiparameterization Land Surface Model (Noah-MP LSM) equipped with a plant hydraulics scheme (Noah-MP-PHS) across 40 FLUXNET sites globally. Employing the Shuffled Complex Evolution-University of Arizona (SCE-UA) auto-calibration algorithm, we optimized key plant hydraulics parameters for these sites spanning eight vegetation types in both arid and humid climates. Noah-MP-PHS significantly improves the simulation of evapotranspiration (ET) and gross primary production (GPP) by better representing atmospheric and soil water stress compared to traditional soil hydraulic schemes (SHSs, such as Noah and CLM). The augmented Noah-MP-PHS models reduce surface flux overestimation and underestimation, exhibiting an average increase of 0.14 and 0.15 in Kling-Gupta Efficiency (KGE) compared to Noah and CLM, respectively. The explicit consideration of plant capacitance in PHS reveals substantial deep-layer and nocturnal root water uptake especially under dry conditions. We employed eXplainable Machine learning (XML) to quantify the model’s relative sensitivity to newly introduced leaf-, stem and root-related parameters in PHS. The sensitivity analysis reveals a rise in root parameter importance and a decline in leaf and stem parameters as conditions shift from humid to arid. These findings indicate that as aridity states vary, the most influential parameters affecting surface fluxes variation may change in parameter calibration for PHS applications. Our findings underscore the importance of incorporating plant hydraulics into LSMs to enhance simulations of terrestrial water and carbon dynamics. These findings are crucial for understanding ecosystem responses to global climate changes and guide the broader application of PHS at larger scales.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Better practices for inferring ecosystem water use strategy from eddy covariance data

Eddy covariance data are critical for inferring ecosystem water use strategies. Yet, such inferences are sensitive to a range of assumptions applied across studies, hindering our understanding of water use strategies within and across eddy covariance sites. A recent analysis across 151 FLUXNET2015 and AmeriFlux-FLUXNET datasets found that poor model performance was the key driver of non-robust inferences of ecosystem water use strategies. Here, we leverage this previous analysis to (i) identify the specific assumptions that improve inference model performance across most sites, (ii) explain the mechanisms behind the performance improvements, and (iii) check whether better performance improves water use inference. We find that the common practice of fitting a model to canopy conductance (G c ) derived from the evapotranspiration (ET) observations, rather than to observed ET itself, artificially amplifies data errors and degrades the model performance. Next, accounting for vegetation dynamics by applying a growing season filter or incorporating satellite LAI data improves performance, but the former practice may remove soil water stress periods. Lastly, using the leaf-to-air vapor pressure deficit (VPD l ) derived from ET observations as a model input may artificially inflate performance. Based on these results, we recommend selecting observed ET (rather than derived G c ) as the response variable, carefully accounting for vegetation dynamics, and avoiding derived VPD l as a model input; these best practices improve model performance by c. 20% and robustness by c. 80% across all eddy covariance sites. Nevertheless, the performance improvements do not always correspond to more robust inference of water use strategies, as model parameter selection and surface energy budget closure corrections still strongly influence the ecosystem water use parameter estimation in a site-specific manner.

AmeriFlux↗

DOE OSTI2023

The neutron number probability distribution in coupled lumped assemblies

Here, the validity of the gamma distribution in describing the neutron number probability distribution function for both isolated and coupled multiplying assemblies when constrained to reproduce the true mean and variance is investigated in lumped geometry by numerical comparison with kinetic Monte Carlo simulations. The mean and variance are obtained from numerical solution of moment equations constructed from the relevant forward Master equation with assembly coupling coefficients obtained from a view factor method. Numerical results for a two-group, two coupled assemblies model, with static and dynamic reactivity insertion, show that except for subcritical assemblies, the gamma distribution well-approximates the number distribution. Differences in the fast and thermal neutron population shapes are explained in terms of effective source strengths due to downscatter and coupling.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2024

Numerical simulation of involute-plate research reactor flow behavior using RANS, LES and DNS

This paper investigates the flow behavior of involute-plate research reactors by performing Reynolds-Averaged Navier Stokes simulation (RANS), Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) of the channel flow between fuel plates. By modeling turbulence with different numerical approaches, this study provides data with three levels of fidelity. For the RANS simulation, three widely used turbulence models, i.e., k-ε, k-ω, Reynolds Stress Turbulence model (RST) are applied by using the commercial CFD code STAR-CCM +. For LES and DNS, the open-source CFD code, Nek5000, is used given its outstanding scalability on High Performance Computer (HPC) and high-order technique. The results from RANS simulations are compared with that from LES and DNS for benchmarking. Both macroscale parameters and turbulence statistics, such as velocity magnitude, lateral velocity and turbulence kinetic energy, are presented and analyzed. The results from RANS simulation achieve good agreement with LES and DNS on velocity and turbulence kinetic energy prediction. The RST turbulence model predicts the most similar flow pattern of lateral velocity as compared to LES and DNS. The Lambda-2 (λ2) criterion with a reasonable threshold is used to demonstrate the instantaneous vortices distribution in the involute channel from both LES and DNS calculation. The DNS simulation captures more detailed turbulence especially near the corner, which explains the discrepancy between LES and DNS results near the corner. The normalized RMS error are defined and calculated to assess the performance of those turbulence models. The RST model captures the anisotropic feature of turbulence, which enable it to outperform other turbulence models for predicting the flow behavior in an involute channel. Although some discrepancies are found between LES and DNS results in the corner, the overall deviations between LES and DNS are found to be small. In conclusion, given that the computational cost of DNS calculation is an order of magnitude higher, using LES data for benchmarking RANS model is a cost-effective approach.

DNS↗

DOE OSTI2020

Optimized Lie–Trotter–Suzuki decompositions for two and three non-commuting terms

Lie–Trotter–Suzuki decompositions are an efficient way to approximate operator exponentials exp ( t H ) when H is a sum of n (non-commuting) terms which, individually, can be exponentiated easily. They are employed in time-evolution algorithms for tensor network states, digital quantum simulation protocols, path integral methods like quantum Monte Carlo, and splitting methods for symplectic integrators in classical Hamiltonian systems. Here, we provide optimized decompositions up to order t 6 . The leading error term is expanded in nested commutators (Hall bases) and we minimize the 1-norm of the coefficients. For n = 2 terms, several of the optima we find are close to those in McLachlan (1995). Generally, our results substantially improve over unoptimized decompositions by Forest, Ruth, Yoshida, and Suzuki. We explain why these decompositions are sufficient to efficiently simulate any one- or two-dimensional lattice model with finite-range interactions. This follows by solving a partitioning problem for the interaction graph.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Role of generic scale invariance in a Mott transition from a U(1) spin-liquid insulator to a Landau Fermi-liquid metal

Highlights: • We look at the role played by generic scale invariance (GSI) in the phase transition between a U(1) spin liquid and a Fermi liquid. • We identify dangerously irrelevant operators in the renormalization group transformation, involved with the GSI. • We highlight novel mean-field dynamics of this Mott quantum criticality, resulting from the GSI. We investigate the role of generic scale invariance in a Mott transition from a U(1) spin-liquid insulator to a Landau Fermi-liquid metal, where there exist massless degrees of freedom in addition to quantum critical fluctuations. Here, the Mott quantum criticality is described by critical charge fluctuations, and additional gapless excitations are U(1) gauge-field fluctuations coupled to a spinon Fermi surface in the spin-liquid state, which turn out to play a central role in the Mott transition. An interesting feature of this problem is that the scaling dimension of effective leading local interactions between critical charge fluctuations differs from that of the coupling constant between U(1) gauge fields and matter-field fluctuations in the presence of a Fermi surface. As a result, there appear dangerously irrelevant operators, which can cause conceptual difficulty in the implementation of renormalization group (RG) transformations. Indeed, we find that the curvature term along the angular direction of the spinon Fermi surface is dangerously irrelevant at this spin-liquid Mott quantum criticality, responsible for divergence of the self-energy correction term in U(1) gauge-field fluctuations. Performing the RG analysis in the one-loop level based on the dimensional regularization method, we reveal that such extremely overdamped dynamics of U(1) gauge-field fluctuations, which originates from the emergent one-dimensional dynamics of spinons, does not cause any renormalization effects to the effective dynamics of both critical charge fluctuations and spinon excitations. However, it turns out that the coupling between U(1) gauge-field fluctuations and both matter-field excitations still persists at this Mott transition, which results in novel mean-field dynamics to explain the nature of the spin-liquid Mott quantum criticality. We discuss physical implications of effective one-dimensional spin dynamics and extremely overdamped gauge dynamics at the Mott quantum criticality.

36 MATERIALS SCIENCE↗