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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 1,153 records · Page 64
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Unravelling competing microscopic interactions at a phase boundary: A single-crystal study of the metastable antiferromagnetic pyrochlore Yb 2 Ge 2 O 7

We report inelastic neutron scattering measurements from our newly synthesized single crystals of the structurally metastable antiferromagnetic pyrochlore Yb 2 Ge 2 O 7 . We determine the four symmetry-allowed nearest-neighbor anisotropic exchange parameters via fits to linear spin wave theory supplemented by fits of the high-temperature specific heat using the numerical linked-cluster expansion method. The exchange parameters so-determined are strongly correlated to the values determined for the g-tensor components, as previously noted for the related Yb pyrochlore Yb 2 Ti 2 O 7 . To address this issue, we directly determined the g-tensor from electron paramagnetic resonance of 1% Yb-doped Lu 2 Ge 2 O 7 , thus enabling an unambiguous determination of the exchange parameters. Our results show that Yb 2 Ge 2 O 7 resides extremely close to the classical phase boundary between an antiferromagnetic Γ 5 phase and a splayed ferromagnet phase. By juxtaposing our results with recent ones on Yb 2 Ti 2 O 7 , our work illustrates that the Yb pyrochlore oxides represent ideal systems for studying quantum magnets in close proximity to classical phase boundaries.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Optimizing Control for Efficient Load Shifting with Thermal Energy Storage in Existing HVAC Systems

This project developed the integration of a direct-contact heat exchanger (DCHX) based thermal energy storage (TES) system with a chiller–air handling unit (AHU) plant to evaluate its potential for reducing building energy costs. Detailed physical models of the TES unit, building envelope, and HVAC components were developed alongside simplified control-oriented models to support both high-fidelity simulation and real-time optimization. Two control strategies were implemented and compared: a rule-based control (RBC) aligned with utility time-of-use (ToU) rates, and a model predictive control (MPC) framework leveraging forecasts of building load, weather, and internal gains.Simulation results show that the RBC strategy reduced daily electricity costs by around 30% by shifting cooling production from on-peak to off-peak hours. In contrast, the MPC strategy achieved significantly greater performance, reducing daily operating costs by up to 44% and peak-hour costs by more than 60%. Both strategies maintained indoor thermal comfort within acceptable limits, with MPC further improving load distribution and reducing equipment cycling.The outcomes confirm that TES integration, particularly when coordinated with advanced predictive control, can provide substantial cost savings and on-peak demand reduction. . These findings directly support the U.S. Department of Energy’s goals for grid-interactive efficient buildings and demonstrate the potential of TES-enabled HVAC systems for scalable deployment across the commercial building.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2023

Water, Ion, and Proton Dynamics and Interactions in Nanoconfined Systems

The research was directed at understanding the role that nanoconfinement has on the dynamics and structure of liquids confined in nanometer size structures. Experiments were conducted using ultrafast infrared methods. The methods were two dimensional infrared (2D IR) spectroscopy and polarization pump-probe (PSPP) experiments. In addition FT-IR spectroscopy was used. To augment the experimental work, high level molecular dynamics simulations of the systems were conducted. The system used for confinement were nanoporous silica with essentially monodispersed pores. Pores of different diameters were studies, i.e., 2.5 nm to 8 nm. Water and organic liquids were investigated. The experiments were performed on a vibrational probe molecule, i.e., the CN stretch of the anion SeCN-. The 2D IR experiments measured spectral diffusion, which directly reported on the structural dynamics of the confined liquids. 2D IR was also used to perform chemical exchange measurements, which observed the formation and dissociation of molecular complexes with surface silanols. The PSPP experiments measured orientational relaxation of the probe molecule as well as it vibrational lifetime. All of the observables depended on the diameter of the pores and the type of liquid. The simulations of the observables provided detailed structural information on the structure of the confined liquids and there interactions with the surfaces. In addition to the study of the confinement in nanopores, water in hydrogels was also studied. The same experimental methods were used along with MD simulations. It was found the influence of hydrogels on water did not come from confinement of the water in the hydrogel polymer network, but rather from the interactions of the water with the individual monomers that compose the polymer. In addition, the temperature dependence of a polymer/water system was tracked from below to above the lower critical solution temperature to observe the nature of the phase separated polymer and how water responded to the phase separation.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Atomic scale understanding of organic anion separations using ion-exchange resins

A combination of ab initio and classical molecular dynamic simulations was used to explore the adsorption/desorption and diffusion characteristics of ion-exchange resins for extraction of organic anions in electrically-driven separation processes. We considered two classes of carboxylate mixtures that are commonly encountered in bioprocessing separations: a short chain fatty acid mixture (acetate/butyrate) and an aromatic mixture (ferulate/coumarate). The suitability of several resin materials including PFC100E, IRC86, PFA444 and IRA67 was interrogated. The decomposition of the interaction energies by the symmetry-adapted perturbation theory and the classical molecular dynamic simulations of organic diffusion together reveal that the geometries of the organic anions and the functional groups of the resins, as well as their Columbic interactions, are the controlling factors in the diffusion process of the organic compounds in these resins. Additionally, classical simulations also show that modifying the functionality of resin beads, the magnitude of electric fields, and the ratio of organic mixtures may provide an effective way to control the diffusion rate and obtain selective separation of these organic mixtures. Finally, a general suggestion for favorable separation conditions is summarized.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Strong Electronic and Magnetic Coupling in M 4 (M = Ni, Cu) Clusters via Direct Orbital Interactions between Low-Coordinate Metal Centers

In this report we present an extensive study of tetranuclear transition-metal cluster compounds M 4 (NP t Bu 3 ) 4 and [M 4 (NP t Bu 3 ) 4 ][B(C 6 F 5 ) 4 ] (M = Ni, Cu; t Bu = tert -butyl), which feature low-coordinate metal centers and direct metal-metal orbital overlap. X-ray diffraction, electrochemical, magnetic, spectroscopic, and computational analysis elucidate the nature of the bonding interactions in these clusters and the impact of these interactions on the electronic and magnetic properties. Direct orbital overlap results in strongly coupled, large-spin ground states in the [Ni 4 (NP t Bu 3 ) 4 ] +/0 clusters and fully delocalized, spin-correlated electrons. Correlated electronic structure calculations confirm the presence of ferromagnetic ground states that arise from direct exchange between magnetic orbitals, and, in the case of the neutral cluster, itinerant electron magnetism similar to that in metallic ferromagnets. The cationic nickel cluster also possesses large magnetic anisotropy exemplified by a large, positive axial zero-field splitting parameter of D = +7.95 or +9.2 cm -1 , as determined by magnetometry or electron paramagnetic resonance spectroscopy, respectively. The [Ni 4 (NP t Bu 3 ) 4 ] + cluster is also the first molecule with easy-plane magnetic anisotropy to exhibit zero-field slow magnetic relaxation, and under a small applied field, it exhibits relaxation exclusively through an Orbach mechanism with a spin relaxation barrier of 16 cm -1 . The S = 1 / 2 complex [Cu 4 (NP t Bu 3 ) 4 ] + exhibits slow magnetic relaxation via a Raman process on the millisecond time scale, supporting the presence of slow relaxation via an Orbach process in the nickel analogue. Overall, this work highlights the unique electronic and magnetic properties that can be realized in metal clusters featuring direct metal-metal orbital interactions between low-coordinate metal centers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

A multirate mass transfer model to represent the interaction of multicomponent biogeochemical processes between surface water and hyporheic zones (SWAT-MRMT-R 1.0)

Abstract. Surface water quality along river corridors can be modulated by hyporheic zones (HZs) that are ubiquitous and biogeochemically active. Watershed management practices often ignore the potentially important role of HZs as a natural reactor. To investigate the effect of hydrological exchange and biogeochemical processes on the fate of nutrients in surface water and HZs, a novel model, SWAT-MRMT-R, was developed coupling the Soil and Water Assessment Tool (SWAT) watershed model and the reaction module from a flow and reactive transport code (PFLOTRAN). SWAT-MRMT-R simulates concurrent nonlinear multicomponent biogeochemical reactions in both the channel water and its surrounding HZs, connecting the channel water and HZs through hyporheic exchanges using multirate mass transfer (MRMT) representation. Within the model, HZs are conceptualized as transient storage zones with distinguished exchange rates and residence times. The biogeochemical processes within HZs are different from those in the channel water. Hyporheic exchanges are modeled as multiple first-order mass transfers between the channel water and HZs. As a numerical example, SWAT-MRMT-R is applied to the Hanford Reach of the Columbia River, a large river in the United States, focusing on nitrate dynamics in the channel water. Major nitrate contaminants entering the Hanford Reach include those from the legacy waste, irrigation return flows (irrigation water that is not consumed by crops and runs off as point sources to the stream), and groundwater seepage resulting from irrigated agriculture. A two-step reaction sequence for denitrification and an aerobic respiration reaction is assumed to represent the biogeochemical transformations taking place within the HZs. The spatially variable hyporheic exchange rates and residence times in this example are estimated with the basin-scale Networks with EXchange and Subsurface Storage (NEXSS) model. Our simulation results show that (1), given a residence time distribution, how the exchange fluxes to HZs are approximated when using MRMT can significantly change the amount of nitrate consumption in HZs through denitrification and (2) source locations of nitrate have a different impact on surface water quality due to the spatially variable hyporheic exchanges.

58 GEOSCIENCES↗
DOE OSTI2020

Simulation of coupled multiphase flow and geomechanics in porous media with embedded discrete fractures

In fractured natural formations, the equations governing fluid flow and geomechanics are strongly coupled. Hydrodynamical properties depend on the mechanical configuration, and they are therefore difficult to accurately resolve using uncoupled methods. In recent years, significant research has focused on discretization strategies for these coupled systems, particularly in the presence of complicated fracture network geometries. In this work, we explore a finite-volume discretization for the multiphase flow equations coupled with a finite-element scheme for the mechanical equations. Fractures are treated as lower dimensional surfaces embedded in a background grid. Interactions are captured using the embedded discrete fracture model (EDFM) and the embedded finite element method (EFEM) for the flow and the mechanics, respectively. This nonconforming approach significantly alleviates meshing challenges. EDFM considers fractures as lower dimension finite volumes that exchange fluxes with the rock matrix cells. The EFEM method provides, instead, a local enrichment of the finite-element space inside each matrix cell cut by a fracture element. Both the use of piecewise constant and piecewise linear enrichments are investigated. They are also compared to an extended finite element approach. One key advantage of EFEM is the element-based nature of the enrichment, which reduces the geometric complexity of the implementation and leads to linear systems with advantageous properties. Synthetic numerical tests are presented to study the convergence and accuracy of the proposed method. It is also applied to a realistic scenario, involving a heterogeneous reservoir with a complex fracture distribution, to demonstrate its relevance for field applications.

58 GEOSCIENCES↗
DOE OSTI2023

Search for non-resonant production of semi-visible jets using Run 2 data in ATLAS

Semi-visible jets, with a significant contribution to the event's missing transverse momentum, can arise in strongly interacting dark sectors. This results in an event topology where one of the jets can be aligned with the direction of the missing transverse momentum. The first search for semi-visible jets produced via a t-channel mediator exchange is presented. The analysis uses proton-proton collisions with an integrated luminosity of 139 fb —1 and a centre-of-mass energy of 13 TeV, collected with the ATLAS detector during the Run 2 of the LHC. No excess over Standard Model predictions is observed. Assuming a coupling strength of unity between the mediator, a Standard Model quark and a dark quark, mediator masses up to 2.7 TeV are excluded at the 95% confidence level. Upper limits on the coupling strength are also derived.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

K–Co–Mo–S x chalcogel: high-capacity removal of Pb 2+ and Ag + and the underlying mechanisms

Chalcogenide-based aerogels, known as chalcogels, represent a novel class of nanoparticle-based porous amorphous materials characterized by high surface polarizability and Lewis base properties, exhibiting promising applications in clean energy and separation science. This work presents a K–Co–Mo–S x (KCMS) chalcogel as a highly efficient sorbent for heavy metal ions and details its sorption mechanisms. Its incoherent structure comprises Mo 2 V (S 2 ) 6 and Mo 3 IV S(S 6 ) 2 anion-like clusters with four- and six-coordinated Co–S polyhedra, forming a Co–Mo–S covalent network that hosts K + ions through electrostatic attraction. The interactions of KCMS with heavy metal ions, particularly Pb 2+ and Ag + , reveal that KCMS is exceptionally effective in removing these ions from ppm concentrations down to trace levels (≤5 ppb). KCMS rapidly removes Ag + (≈81.7%) and Pb 2+ (≈99.5%) within five minutes, achieving >99.9% removal within an hour, with a distribution constant K d ≥10 8 mL g -1 . KCMS exhibits an impressive removal capacity of 1378 mg g -1 for Ag + and 1146 mg g -1 for Pb 2+ , establishing it as one of the most effective materials known to date for heavy metal removal. This material is also effective for the removal of Ag + and Pb 2+ along with Hg 2+ , Ni 2+ , Cu 2+ , and Cd 2+ from various water sources even in the presence of highly concentrated and chemically diverse cations, anions, and organic species. Analysis of the post-interacted KCMS by synchrotron X-ray pair distribution function (PDF), X-ray photoelectron spectroscopy (XPS) and energy dispersive X-ray spectroscopy (EDS) revealed that the sorption of Pb 2+ , Ag + , and Hg 2+ mainly occurs by the exchange of K + and Co 2+ . Despite being amorphous, this material exhibits unprecedented ion-exchange mechanisms both for the ionically and covalently bound K + and Co 2+ , respectively. In conclusion, this discovery advances our knowledge of amorphous gels and guides material synthesis principles for the highly selective and efficient removal of heavy metal ions from water.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

Electrons and Phonons Cooperate in the Laser-Induced Desorption of CO from Pd(111)

Femtosecond laser induced desorption of CO from a CO-covered Pd(111) surface is explored with ab initio molecular dynamics with electronic friction that incorporates effects due to the excited electronic and phononic systems, as well as out-of-phase coadsorbate interactions. Our simulations reflect evidence of an important electron-phonon synergy in promoting CO desorption that has largely been neglected in other similar systems. At the saturated coverage of 0.75 ML, effects due to CO-CO interadsorbate energy exchange are also important. Our dynamics simulations, in concert with site-specific desorption energy calculations, enable us to understand the large coverage dependence of the desorption yields observed in experiments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Ultrafast Electron Correlations and Memory Effects at Work: Femtosecond Demagnetization in Ni

Experimental observations of the ultrafast (less than 50 fs) demagnetization of Ni have so far defied theoretical explanations particularly since its spin-flipping time is much less than that resulting from spin-orbit and electron-lattice interactions. Through the application of an approach that benefits from spin-flip time-dependent density-functional theory and dynamical mean-field theory, we show that proper inclusion of electron correlations and memory (time dependence of electron-electron interaction) effects leads to demagnetization at the femtosecond scale, in good agreement with experimental observations. Furthermore, our calculations reveal that this ultrafast demagnetization results mainly from spin-flip transitions from occupied to unoccupied orbitals implying a dynamical reduction of exchange splitting. In this work, these conclusions are found to be valid for a wide range of laser pulse amplitudes. They also pave the way for ab initio investigations of ultrafast charge and spin dynamics in a variety of quantum materials in which electron correlations may play a definitive role.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Data Needs for Modeling Low-Temperature Non-Equilibrium Plasmas: The LXCat Project, History, Perspectives and a Tutorial

Technologies based on non-equilibrium, low-temperature plasmas are ubiquitous in today’s society. Plasma modeling plays an essential role in their understanding, development and optimization. An accurate description of electron and ion collisions with neutrals and their transport is required to correctly describe plasma properties as a function of external parameters. LXCat is an open-access, web-based platform for storing, exchanging and manipulating data needed for modeling the electron and ion components of non-equilibrium, low-temperature plasmas. The data types supported by LXCat are electron- and ion-scattering cross-sections with neutrals (total and differential), interaction potentials, oscillator strengths, and electron- and ion-swarm/transport parameters. Online tools allow users to identify and compare the data through plotting routines, and use the data to generate swarm parameters and reaction rates with the integrated electron Boltzmann solver. In this review, the historical evolution of the project and some perspectives on its future are discussed together with a tutorial review for using data from LXCat.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Critical Evaluation of a Novel Analysis Technique for Assessment of Printed Circuit Heat Exchangers in High-Temperature Nuclear Service

Application of printed circuit heat exchangers (PCHEs) to very high-temperature reactors (VHTRs) requires mechanical performance assessment methodologies. The PCHE morphology consists of thousands of millimeter-scale channels, for enhanced thermal efficiency, enclosed in a meter-scale PCHE core. PCHE geometry under thermomechanical creep-fatigue transients results in multi-axial interactions between its different segments, such as channeled core, walls, and headers. These global-level interactions influence the local channel-level responses. Hence, developing a PCHE performance assessment methodology, following the ASME Code, Section III, Division 5 provisions, is a critical gap to be filled. There is no analysis or design methodology available in ASME Code to assess a PCHE for its global and local level performances under high temperature and pressure loadings. This paper critically evaluates a recently proposed two-step analysis technique to estimate global interactions and local channel-level responses of PCHEs. In this novel analysis technique, the channeled PCHE core is replaced with orthotropic solid blocks of representative stiffness properties for the global thermomechanical analysis. Here, subsequent channel scale submodel analysis with detailed channel geometry, loading, and elastic-perfectly plastic (EPP) material model estimates the local responses for PCHE performance assessment. This paper critically evaluates this novel technique for its effectiveness in PCHE performance assessment. Finite element (FE) models imitating various analysis issues are developed, and FE analysis results are scrutinized. An important outcome of this study is the validation of the novel two-step PCHE analysis technique for application to the performance assessment of PCHEs in VHTRs.

42 ENGINEERING↗
DOE OSTI2025

The Role of Water Volume Fraction on Water Adsorption in Anion Exchange Membranes

Water absorption plays a key role in the performance of polymeric anion exchange membranes. It influences important properties such as ionic conductivity and mechanical strength and alters their performance as solid electrolytes in hydrogen electrochemical devices for energy conversion. However, computational approaches that address the relationship between the polymer design and the absorption process are scarce. In this work, we introduce a simple thermodynamic model to predict the water absorption isotherms of polyelectrolyte membranes in contact with a water vapor reservoir that incorporates the specific chemical design of the polymers. The model accurately predicts the water content and macrostructural properties of polynorbornene membranes as a function of the water activity and successfully captures the effect of various polymer design parameters. The energy of pairwise attractive interactions predicted by our model provides a means to interpret the absorption process at the molecular level. The model also reveals the most significant favorable and unfavorable contributions to the free energy and indicates that their balance is solely governed by the water volume fraction, regardless of the polymer design. This universal behavior leads to important implications in the search for better ion exchange membranes.

Zaldivar, Gervasio [New York University, Brooklyn,↗
DOE OSTI2024

Effects of boundary hydraulics, dissolved oxygen, and dissolved organic carbon on growth and death dynamics of aerobic microbes in riverbed dune-induced hyporheic zones

Surface and groundwater interact in the hyporheic zone beneath and adjacent to rivers in the presence of a diverse microbial community. Heterotrophic bacteria mediate a range of environmentally important reactions, yet few studies have quantified bacterial growth and death dynamics in the hyporheic zone, and none have systematically analyzed their response to variations in hydraulic or chemical conditions. Here we used MODFLOW and SEAM3D to simulate hydraulics; dissolved oxygen (DO) and dissolved organic carbon (DOC) transport; and aerobic microbial metabolism, growth, and death in hyporheic zones induced by riverbed dunes. We ran simulations both with and without growth/death processes, and varied hydraulic parameters and DO/DOC boundary concentrations. Microbial biomass reached steady state (t = 3 days) in every simulation, at which time there was greater biomass and DOC biodegradation rates in the hyporheic flowcell (300% and 85% higher for the base case, respectively) when accounting for microbial growth dynamics. This occurred as microbial biomass tailored its spatial distribution to the availability of DO and DOC, demonstrating the importance of simulating growth/death processes. Biomass generally increased with hyporheic flow cell area as upwelling groundwater decreased. When varying surface water DO and DOC source concentrations relative to the base case, the greatest effect on biomass occurred when increasing DOC and decreasing DO. We determined minimum DO and DOC steady-state concentrations required for microbial growth, but the minimums were not absolute or related by stoichiometry. Increasing DOC created a smaller area of microbes with higher concentrations relative to the base case. Increasing DO slightly increased the area occupied by microbes while keeping the total biomass nearly constant. Overall, microbial growth and death dynamics depend on DO and DOC availability in the hyporheic zone, which is dependent on DOC/DO boundary concentrations and hyporheic flow paths, and in turn the hydraulic interaction between surface water and groundwater.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Chapter 9.12 - Weather, Climatic and Ecological Impacts of Onshore Wind Farms

Wind power is an environmentally sustainable technology that is likely to be part of the solution to the climate change, air pollution, and energy security problems. Despite many positive benefits, the rapid development of wind power has raised concerns about some potential adverse environmental impacts. While converting wind?s kinetic energy into electricity, wind turbines (WTs) modify properties of the atmospheric boundary layer (ABL) including the vertical profiles and surface-atmosphere exchanges of energy, momentum, mass, moisture, and trace gases. Given the current installed capacity and the projected installation worldwide, wind farms (WFs) are likely becoming a major driver of manmade land use change on Earth. Hence, understanding WT-atmosphere-surface interactions and assessing potential environmental impacts of WFs are of significant scientific, societal and economic importance. Here we review our progress in assessing potential impacts of onshore wind power on weather, climate and vegetation activity. A consensus is emerging based on observations and modeling studies that WFs cause a local to regional warming effect, particularly at nighttime, while the impacts on precipitation, wind patterns, crop yields and vegetation activity are uncertain. The warming effect results simply from vertical heat redistribution within the ABL due to turbine-enhanced vertical turbulent mixing in the wakes. At the global scale, with a substantial installation of WFs, mesoscale and climate models predicted large regional changes but small global impacts on temperature, while the impacts on precipitation, clouds, wind patterns and large-scale circulation have large uncertainties and are region specific and scale dependent. Despite increasing number of research efforts, our assessment of potential WF impacts is still very limited. Although the WF impacts are mostly local and limited to the near-surface ABL, this is the layer where we live and plants grow. Hence, more studies are needed to improve our understanding of WT-atmosphere-surface interactions and our capability to model and project the weather, climatic and ecological impacts of large WFs.

atmospheric boundary layer↗
DOE OSTI2020

Automated calculation and convergence of defect transport tensors

Defect diffusion is a key process in materials science and catalysis, but as migration mechanisms are often too complex to enumerate a priori, calculation of transport tensors typically have no measure of convergence and require significant end-user intervention. These two bottlenecks prevent high-throughput implementations essential to propagate model-form uncertainty from interatomic interactions to predictive simulations. In order to address these issues, we extend a massively parallel accelerated sampling scheme, autonomously controlled by Bayesian estimators of statewide sampling completeness, to build atomistic kinetic Monte Carlo models on a state-space irreducible under exchange and space group symmetries. Focusing on isolated defects, we derive analytic expressions for drift and diffusion coefficients, providing a convergence metric by calculating the Kullback–Leibler divergence across the ensemble of diffusion processes consistent with the sampling uncertainty. The autonomy and efficacy of the method is demonstrated on surface trimers in tungsten and Hexa-interstitials in magnesium oxide, both of which exhibit complex, correlated migration mechanisms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Spin-1 Kitaev-Heisenberg model on a honeycomb lattice

We study the Kitaev-Heisenberg model with spin-1 local degree of freedom on a honeycomb lattice numerically by the infinite density matrix renormalization group method on a cylinder geometry. By tuning the relative value of the Kitaev and Heisenberg exchange couplings, we obtain the phase diagram with two spin liquid phases and four symmetry-broken phases. Here, we identify that the spin liquid phases are gapless by calculating the central charge at the pure Kitaev points without the Heisenberg interactions. Comparing to its spin-1/2 counterpart, the position and number of gapless modes of the spin-1 case are quite different. Due to the approximate Z 2 local conservations, the expectation value of the Wilson loop operator measuring the flux of each plaquette stays near to 1, and the static spin-spin correlations remain short range in the entire spin liquid phases.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗