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At least 397 records · Page 22

Liquid Phase Modeling in Porous Media: Adsorption of Methanol and Ethanol in H-MFI in Condensed Water

Zeolites are used in the chemical and separation industries for their exceptional selectivity, adsorption capacity, regenerability, and stability in gas and liquid phase processing. Here, we developed an explicit solvation method for predicting solvent/condensed phase effects on adsorption free energies in microporous media such as zeolites based on the hybrid quantum mechanical/molecular mechanical free energy perturbation (QM/MM-FEP) technique. Our explicit solvation method for zeolite systems, called eSZS, aims to capture site-specific interactions during the adsorption process at the Brønsted acid sites of H-MFI zeolite while still considering the diverse configuration space of the solvent molecules. This strategy is ideal for chemical reactions or adsorbates that interact with the microporous medium in few distinct adsorbate/transition state configurations, i.e., the harmonic or similar approximations are acceptable for the adsorbate/transition state while such approximations break down for the solvent molecules that require extensive configuration space sampling. In this way, our approach effectively overcomes the limitations of implicit solvation models and classical force field methods for describing solvation effects on chemical reactions within porous materials such as zeolites. Specifically, in this study, we investigated various aspects of our hybrid QM/MM approach, including QM cluster size dependencies in a periodic electrostatically embedded cluster model (PEECM), rules for link atoms at the QM/MM boundary, and functional and basis set considerations for converged and reasonably accurate gas and aqueous phase methanol and ethanol adsorption free energy predictions in H-MFI. For gas phase adsorption of methanol and ethanol in H-MFI at a Brønsted acid site in T12 position, we compute adsorption free energies at 298 K of −0.61 and −0.75 eV, respectively, using a PEECM containing 50 Si and 1 Al atom with ωB97x-D/def2-TZVP level of theory. For solvent effect calculations, we sample the aqueous phase using grand canonical Monte Carlo (GCMC) simulations to (1) obtain a mean field of electrostatic interactions in the reaction system and (2) perform a rigorous free energy perturbation calculation. Similar to the experimentally and computationally observed endergonic solvation effects observed for hydrocarbon adsorption on metal surfaces, we also observe that a condensed aqueous environment destabilizes methanol and ethanol at these acid sites in H-MFI at 298 K. Specifically, the computed solvation free energies of adsorption (ΔΔG solv ) for methanol and ethanol are +0.44 and +0.54 eV, respectively. From this study, it is evident that adsorbates (methanol and ethanol) are competing with water for adsorption space inside the H-MFI zeolite, leading to an endergonic solvation effect. Here, we expect that the endergonic, aqueous solvent effect during adsorption in microporous zeolites is highly tunable by changing the pore size and hydrophobicity of the microporous material as this will affect the water density inside the pore structure.

Adsorption↗

Modeling quasielastic interactions of monoenergetic kaon decay-at-rest neutrinos

Monoenergetic muon neutrinos at 236 MeV are readily produced in intense medium-energy proton facilities (≳2–3GeV) when a positive kaon decays at rest (KDAR; K + →μ + ν μ ). These neutrinos provide a unique opportunity to both study the neutrino interaction and probe the nucleus with a monoenergetic weak-interaction-only tool. We present cross-section calculations for quasielastic scattering of these 236-MeV neutrinos off 12 C and 40 Ar, paying special attention to low-energy aspects of the scattering process. Our model takes the description of the nucleus in a mean-field approach as the starting point, where we solve Hartree-Fock equations using a Skyrme type nucleon-nucleon interaction. Thereby, we introduce long-range nuclear correlations by means of a continuum random-phase approximation (CRPA) framework where we solve the CRPA equations using a Green's function method. The model successfully describes (e,e') data on 12 C and 40 Ca in the kinematic region that overlaps with the KDAR ν μ phase space. In addition to these results, we present future prospects for precision KDAR cross-section measurements and applications of our calculations in current and future experiments that will utilize these neutrinos.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Machine learning the electric field response of condensed phase systems using perturbed neural network potentials

Abstract The interaction of condensed phase systems with external electric fields is of major importance in a myriad of processes in nature and technology, ranging from the field-directed motion of cells (galvanotaxis), to geochemistry and the formation of ice phases on planets, to field-directed chemical catalysis and energy storage and conversion systems including supercapacitors, batteries and solar cells. Molecular simulation in the presence of electric fields would give important atomistic insight into these processes but applications of the most accurate methods such as ab-initio molecular dynamics (AIMD) are limited in scope by their computational expense. Here we introduce Perturbed Neural Network Potential Molecular Dynamics (PNNP MD) to push back the accessible time and length scales of such simulations. We demonstrate that important dielectric properties of liquid water including the field-induced relaxation dynamics, the dielectric constant and the field-dependent IR spectrum can be machine learned up to surprisingly high field strengths of about 0.2 V Å −1 without loss in accuracy when compared to ab-initio molecular dynamics. This is remarkable because, in contrast to most previous approaches, the two neural networks on which PNNP MD is based are exclusively trained on molecular configurations sampled from zero-field MD simulations, demonstrating that the networks not only interpolate but also reliably extrapolate the field response. PNNP MD is based on rigorous theory yet it is simple, general, modular, and systematically improvable allowing us to obtain atomistic insight into the interaction of a wide range of condensed phase systems with external electric fields.

Science & Technology - Other Topics↗

Comparison of the dielectric and magnetocaloric properties of bulk and film of GdFe 0.5 Cr 0.5 O 3

Here, we report a comparison of the magnetic, magnetocaloric, and dielectric properties of 50% iron substituted GdCrO 3 (GdFe 0.5 Cr 0.5 O 3 ) bulk pellet and 960 nm thick film of GdFe 0.5 Cr 0.5 O 3 (GFCO). The 960 nm film was synthesized on a platinized-silicon substrate by chem. soln. deposition and spin-coating methods. The X-ray diffraction scans of the bulk sample and the film as well as the morphology of the film as examined by the field-emission scanning electron microscope indicate phase-pure and polycrystalline nature of these samples. XPS was used to deermine the valence states of Gd, Fe, and Cr. The temp. dependence of the dielectric const. from 225 to 700 K shows peaks at T C = 525 K for the bulk and ≈450 K for the film due to ferroelectric to paraelectric transitions, since elec. polarization vs elec. field hysteresis loops are observed. at room temp. The dielectric studies in the bulk GFCO for T > T C indicate a relaxor-like behavior. The measurements of the magnetization (M) of the samples as a function of temp. (5-350 K) and magnetic field (H) up to 7 T (=70 kOe) depict hysteresis behavior at low temps. due to the canted antiferromagnetic order of Fe 3+ /Cr 3+ below the Néel temp. of ≈275 K. The M vs H isotherms at various temps. are used to det. and compare the magnetic entropy change (-ΔS) and relative cooling power (RCP) of the two samples, yielding (-ΔS) = 30.7 J/kg K (18.8 J/kg K) and RCP = 566.5 J/kg (375 J/kg) for the bulk (960 nm film) samples of GFCO at 7 K and 7 T, resp. The plot of RCP vs T shows that magnetic cooling for this system is most effective for T < 30 K. Comparatively smaller magnitudes of (-ΔS) and RCP for the film vis-a-vis the bulk sample of GFCO scale with its reduced magnetization. This suggests that further improvements in the quality of the films are needed to improve their magnetization and hence their magnetocaloric properties, possibly making them useful for on-chip cooling in miniaturized devices.

36 MATERIALS SCIENCE↗

Many routes to ferroelectric HfO 2 : A review of current deposition methods

Although 10 years have passed since the initial report of ferroelectricity in hafnia (HfO 2 ), researchers are still intensely fascinated by this material system and the promise it holds for future applications. A wide variety of deposition methods have been deployed to create ferroelectric HfO 2 thin films such as atomic layer deposition, chemical solution deposition, and physical vapor deposition methods such as sputtering and pulsed laser deposition. Process and design parameters such as deposition temperature, precursor choice, target source, vacuum level, reactive gases, substrate strain, and many others are often integral in stabilizing the polar orthorhombic phase and ferroelectricity. We examine processing parameters across four main different deposition methods and their effect on film microstructure, phase evolution, defect concentration, and resultant electrical properties. The goal of this review is to integrate the process knowledge collected over the past 10 years in the field of ferroelectric HfO 2 into a single comprehensive guide for the design of future HfO 2 -based ferroelectric materials and devices.

36 MATERIALS SCIENCE↗

Post-fire soil respiration in late growing season (2023 and 2024), Kougarok Fire Complex, Seward Peninsula, Alaska

Field soil respiration data collected in 2023 and 2024 from burned and unburned tussock tundra sites in the Kougarok Fire Complex, near Nome, on the Seward Peninsula of Alaska. Specifically, we measured soil properties and late-growing season CO2 fluxes in patches of unique plant functional types (forbs, shrubs, and graminoids) across two years in tundra recovering from repeated wildfires over the decade. The goal was to identify the main drivers of soil respiration in Arctic tundra underlain by discontinuous permafrost that is recovering from two recent, repeated wildfires that differed in fire age and number of times burned, thereby resulting in different levels of vegetation and subsurface property changes (i.e., successional trajectories). There are five files in *.csv format with one data file and four data description files including data, dictionary, methods, terminology, and file-level metadata. The Next-Generation Ecosystem Experiments: Arctic (NGEE Arctic), is a research effort to reduce uncertainty in Earth System Models by developing a predictive understanding of carbon-rich Arctic ecosystems and feedbacks to climate. NGEE Arctic was supported by the Department of Energy's Office of Biological and Environmental Research. The NGEE Arctic Phase 3 project had two field research sites: 1) located within the Arctic polygonal tundra coastal region on the Barrow Environmental Observatory (BEO) and the North Slope near Utqiagvik (Barrow), Alaska and 2) multiple areas on the discontinuous permafrost region of the Seward Peninsula north of Nome, Alaska. Through observations, experiments, and synthesis with existing datasets, NGEE Arctic provided an enhanced knowledge base for multi-scale modeling and contributed to improved process representation at global pan-Arctic scales within the Department of Energy's Earth system Model (the Energy Exascale Earth System Model, or E3SM), and specifically within the E3SM Land Model component (ELM).

Santos, Fernanda [ORNL] (ORCID:0000000191555623)↗

Floating Block Method for Quantum Monte Carlo Simulations

Quantum Monte Carlo simulations are powerful and versatile tools for the quantum many-body problem. In addition to the usual calculations of energies and eigenstate observables, quantum Monte Carlo simulations can in principle be used to build fast and accurate many-body emulators using eigenvector continuation or design time-dependent Hamiltonians for adiabatic quantum computing. Furthermore, these new applications require something that is missing from the published literature, an efficient quantum Monte Carlo scheme for computing the inner product of ground state eigenvectors corresponding to different Hamiltonians. In this work, we introduce an algorithm called the floating block method, which solves the problem by performing Euclidean time evolution with two different Hamiltonians and interleaving the corresponding time blocks. We use the floating block method and nuclear lattice simulations to build eigenvector continuation emulators for energies of 4 He, 8 Be, 12 C, and 16 O nuclei over a range of local and nonlocal interaction couplings. From the emulator data, we identify the quantum phase transition line from a Bose gas of alpha particles to a nuclear liquid.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Electric-Field Manipulation of Magnetic Chirality in a Homo-Ferro-Rotational Helimagnet

Ferro-rotational (FR) materials, renowned for their distinctive material functionalities, present challenges in the growth of homo-FR crystals (i.e., single FR domain). This study explores a cost-effective approach to growing homo-FR helimagnetic RbFe(SO 4 ) 2 (RFSO) crystals by lowering the crystal growth temperature below the T FR threshold using the high-pressure hydrothermal method. Through polarized neutron diffraction experiments, it is observed that nearly 86% of RFSO crystals consist of a homo-FR domain. Notably, RFSO displays remarkable stability in the FR phase, with an exceptionally high T FR of ≈573 K. Furthermore, RFSO exhibits a chiral helical magnetic structure with switchable ferroelectric polarization below 4 K. Importantly, external electric fields can induce a single magnetic domain state and manipulate its magnetic chirality. The findings suggest that the search for new FR magnets with outstanding material properties should consider magnetic sulfates as promising candidates.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Impacts of Synoptic-Scale Dynamics on Clouds and Radiation in High Southern Latitudes

High-latitudinal mixed-phase clouds significantly affect Earth's radiative balance. Observations of cloud and radiative properties from two field campaigns in the Southern Ocean and Antarctica were compared with two global climate model simulations. A cyclone compositing method was used to quantify “dynamics-cloud-radiation” relationships relative to the extratropical cyclone centers. Observations show larger asymmetry in cloud and radiative properties between western and eastern sectors at McMurdo compared with Macquarie Island. Most observed quantities at McMurdo are higher in the western (i.e., post-frontal) than the eastern (frontal) sector, including cloud fraction, liquid water path (LWP), net surface shortwave and longwave radiation (SW and LW), except for ice water path (IWP) being higher in the eastern sector. Here, the two models were found to overestimate cloud fraction and LWP at Macquarie Island but underestimate them at McMurdo Station. IWP is consistently underestimated at both locations, both sectors, and in all seasons. Biases of cloud fraction, LWP, and IWP are negatively correlated with SW biases and positively correlated with LW biases. The persistent negative IWP biases may have become one of the leading causes of radiative biases over the high southern latitudes, after correcting the underestimation of supercooled liquid water in the older model versions. By examining multi-scale factors from cloud microphysics to synoptic dynamics, this work will help increase the fidelity of climate simulations in this remote region.

58 GEOSCIENCES↗

Findings on subtask 1.6 – basin electric carbon storage research project: novel monitoring techniques

The Energy & Environmental Research Center (EERC) led a study to validate novel and emerging technologies as commercial monitoring techniques for application in carbon dioxide (CO 2 ) injection operations. This applied research was conducted at Basin Electric Power Cooperative’s (Basin Electric’s) active CO 2 -injection operations in Beulah, North Dakota, in two phases. The EERC previously completed a set of baseline (preinjection) activities in Phase 1, which included 1) design of an automated, integrated, modular (AIM) monitoring station; 2) time-lapse electromagnetic (EM) field surveys; 3) drone-based surveillance studies; 4) time-lapse monitoring with seismic methods; and 5) advanced wellbore-monitoring methods.

54 ENVIRONMENTAL SCIENCES↗

Spatial Mapping of Electrostatic Fields in 2D Heterostructures

In situ electron microscopy is an effective tool for understanding the mechanisms driving novel phenomena in 2D structures. However, due to practical challenges, it is difficult to address these technologically relevant 2D heterostructures with electron microscopy. Here, we use the differential phase contrast (DPC) imaging technique to build a methodology for probing local electrostatic fields during electrical operation with nanoscale spatial resolution in such materials. We find that, by combining a traditional DPC setup with a high-pass filter, we can largely eliminate electric fluctuations emanating from short-range atomic potentials. Using a method based on this filtering algorithm, a priori electric field expectations can be directly compared with experimentally derived values to readily identify inhomogeneities and potentially problematic regions. Furthermore, we use this platform to analyze the electric field and charge density distribution across layers of hBN and MoS 2 .

79 ASTRONOMY AND ASTROPHYSICS↗

Role of spin-orbit coupling on crystal-field splitting and phase-stability of rare-earth based layered intermetallic

Layered and incommensurate heterostructures have attracted much attention for the occurrence of superconductivity and charge density waves with the possibility of intercalating foreign atoms. However, lanthanide-based heterostructures where (Eu x Sm 1-x )S and TaS 2 are alternatively stacked have been scarcely investigated. In this work, we performed phase stability, bonding behavior and electronic-structure analysis of (Eu x Sm 1-x )TaS 3 using first-principles density-functional theory methods. Our phase stability analysis suggests 50 at.% solubility of Eu in (Eu x Sm 1-x )TaS 3 compared to Eu solubility in all proportions in cubic SmS. The instability of Eu beyond 50 at.% in (Eu x Sm 1-x )TaS 3 was attributed to higher density of Eu-4f states at the Fermi-level. Based on band position calculated from spin-orbit coupling effect, we constructed a qualitative schematic of possible crystal-field analysis. The local change in bond-length and bond-angle around Eu-S in (Eu x Sm 1-x )TaS 3 correlate well with our crystal-field analysis. We believe that quantum mechanical insights provided in this work will be useful to understand other complex heterostructures.

36 MATERIALS SCIENCE↗

Surrogate models for linear response

Linear response theory is a well-established method in physics and chemistry for exploring excitations of many-body systems. In particular, the quasiparticle random-phase approximation (QRPA) provides a powerful microscopic framework by building excitations on top of the mean-field vacuum; however, its high computational cost limits model calibration and uncertainty quantification studies. Here, we present two complementary QRPA surrogate models and apply them to study response functions of finite nuclei. One is a reduced-order model that exploits the underlying QRPA structure, while the other utilizes the recently developed parametric matrix model algorithm to construct a map between the system’s Hamiltonian and observables. Our benchmark applications, the calculation of the electric dipole polarizability of 180 Yb and the 𝛽-decay half-life of 80 Ni, show that both emulators can achieve 0.1%–1% accuracy while offering a 6–7 orders of magnitude speedup compared to state-of-the-art QRPA solvers. These results demonstrate that the developed QRPA emulators are well positioned to enable Bayesian calibration and large-scale studies of computationally expensive physics models describing the properties of many-body systems.

Beta decay↗

Microscopic characterization of Ising conformal field theory in Rydberg chains

Rydberg chains provide an appealing platform for probing conformal field theories (CFTs) that capture universal behavior in a myriad of physical settings. Focusing on a Rydberg chain at the Ising transition separating charge density wave and disordered phases, we establish a detailed link between microscopics and low-energy physics emerging at criticality. Here, we first construct lattice incarnations of primary fields in the underlying Ising CFT including chiral fermions, a nontrivial task given that the Rydberg chain Hamiltonian does not admit an exact fermionization. With this dictionary in hand, we compute correlations of microscopic Rydberg operators, paying special attention to finite, open chains of immediate experimental relevance. We further develop a method to quantify how second-neighbor Rydberg interactions tune the sign and strength of four-fermion couplings in the Ising CFT. Finally, we determine how the Ising fields evolve when four-fermion couplings drive an instability to Ising tricriticality. Our results pave the way to a thorough experimental characterization of Ising criticality in Rydberg arrays and can inform the design of novel higher-dimensional phases based on coupled critical chains.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Exploration of a Novel Technique for Waste Heat Recovery Through Molecular Dynamics: Influence of Wettability and Electric Field on Water and Water-Based Nanofluids

Most of the energy produced globally comes by way of a heat engine. The Carnot principle places a limit as to how thermodynamically efficient a heat engine can be. There is no heat engine that can be 100% thermodynamically efficient and as such a substantial proportion of all heat supplied to a heat engine is lost as waste heat. Waste heat therefore is a large energy source ready to be properly utilized. Herein, a novel approach for converting waste heat to electricity is discussed. It involves the use of the liquid to vapor phase change of a material dielectric (water) or electrolyte (nanofluid) in the embodiment of a capacitor for direct thermal to electrostatic energy conversion. While this method of waste heat recovery could potentially be added to the ever expanding portfolio of energy conversion techniques, a number of aspects must be addressed before it can be brought into practice. Water was seen as an ideal dielectric phase change material given its high relative permittivity ratio when in the liquid form as compared to its vapor form. However, given its short voltage holdoff time the phase change of water would need to occur rapidly. This brings up concerns of explosive boiling. Herein, molecular dynamics analysis into the explosive boiling behavior of thin water films gave more insight into how the interaction between the surface and liquid affected explosive boiling onset time. A Lennard-Jones potential with one interaction site and a Morse potential with three interaction sites between water and solid substrate were used. It was found generally that a stronger interaction between water film and substrate led to faster explosive boiling onset times but an increase in the number of interaction sites delayed explosive boiling, even at the same wettability (contact angle). Understanding changes in the density and enthalpy of vaporization of a liquid dielectric such as water in the presence of an electric field is of importance due to the electrostatic nature of the waste heat conversion method under consideration. Specifically, if both density and enthalpy of vaporization are increased, the thermodynamic efficiency of the waste heat conversion method under consideration is decreased. Electric field effects are explored herein via molecular dynamics using two water models, the TIP4P-Ew and SWM4-NDP. The SWM4-NDP model is polarizable while the TIP4P-Ew model is not, which allows for a determination of the importance of model polarizability (i.e. variation in water model dipole moment) on these two properties of water when subjected to an electric field. Herein it was found that both water models respond similarly in terms of density and vaporization enthalpy variance upon the introduction of an electric field. Comparison was also made to the pressure induced by the electric field (electrostriction pressure) by way of a density comparison and it was found that the predicted electrostriction pressure overestimates the pressure experienced by water. Water by itself has a high enthalpy of vaporization, which limits the efficiency of the newly proposed conversion method. Research both experimental and through simulation has shown that the vaporization enthalpy of nanofluids can be engineered via nanoparticle size and material selection. An avenue less explored is manipulating the enthalpy of vaporization by altering the interaction strength between the nanoparticles and the base fluid. In practice this could be achieved through the addition of coatings to the nanoparticles to alter their wettability to the base fluid. This was explored by using a Lennard-Jones potential and Morse potential to model the interaction between base fluid (water) and the nanoparticle. For nanoparticles 2nm in diameter and at weight percentages up to 6%, the change in vaporization enthalpy due to alterations of the interaction strength between nanoparticle and base fluid was not significant (less than a 1% difference) when compared to the effect of altering the weight percentage of nanoparticles in the nanofluid or introducing an electric field. However, the effect of wettability may still become important at other nanoparticle concentrations and sizes. In all, the studies presented here further the understanding of phase change and thermodynamic properties of water and water based nanofluids under an electrostatic field which will help inform the development of a novel approach to waste heat conversion. The reduction of waste heat will improve energy sustainability outlooks.

30 DIRECT ENERGY CONVERSION↗

Anisotropic index of refraction and structural properties of hexagonal boron nitride epilayers probed by spectroscopic ellipsometry

The anisotropic index of refraction of 200 μm thick boron-10 enriched hexagonal boron nitride (h-BN) freestanding epilayers grown by metalorganic chemical vapor deposition has been measured using spectroscopic ellipsometry in the UV (4.0–5.1 eV) spectral range. It was found that the index of refraction for the polarization mode with an electric field perpendicular to the c-axis (ordinary, n o ) is much higher than that with an electric field parallel to the c-axis (extraordinary, n e ). By inclusion of turbostratic- (t-) phase layers within h-BN having an average inclination angle (θ) with respect to the ideal c-plane, a simple method for quantifying θ has been deduced. Our results revealed that the presence of t-phase layers decreases the optical anisotropy of h-BN and that a signature of improved crystalline quality is an increase in the ordinary index of refraction (n o ) as a result of the average incline angle θ approaching 0° and predicted that n o = 2.7 and n e = 1.5 at 280 nm for single crystalline h-BN epilayers. More importantly, our results demonstrated that spectroscopic ellipsometry is an effective technique for characterizing the crystalline quality of h-BN epilayers with the advantages of being noninvasive and highly sensitive.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Neutral beam prompt loss in LTX-β

Prompt loss of beam injected fast ions approaches 100% in lithium tokamak experiment-beta (LTX-β) discharges, though significantly improved confinement is expected for the higher current plasmas made available by a recent upgrade to the Ohmic heating power supply. Modeling of fast ions using TRANSP/NUBEAM finds a maximum coupled beam fraction of 76% at the near-term limits of the LTX-β operating space. The full ion orbit code POET is employed to validate NUBEAM results against possible non-adiabatic effects on fast ion orbits, but corrections to the prompt loss fraction due to collisionless transport are found to be small. The graphical method code CONBEAM is used to investigate the topology of fast ion phase space as it relates to neutral beam deposition, and counter-injected NBI is considered as a way to access a region of high field side beam deposition. A metric is developed within the CONBEAM using a beam filament model to estimate the prompt loss fraction and shown to agree well with both POET and NUBEAM, enabling near real-time analysis and potential feedback to operators between plasma discharges.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Universal Tripartite Entanglement in One-Dimensional Many-Body Systems

Motivated by conjectures in holography relating the entanglement of purification and reflected entropy to the entanglement wedge cross section, we introduce two related non-negative measures of tripartite entanglement g and h. We prove structure theorems which show that states with nonzero g or h have nontrivial tripartite entanglement. We then establish that in one dimension these tripartite entanglement measures are universal quantities that depend only on the emergent low-energy theory. For a gapped system, we argue that either g≠0 and h=0 or g=h=0, depending on whether the ground state has long-range order. For a critical system, we develop a numerical algorithm for computing g and h from a lattice model. We compute g and h for various CFTs and show that h depends only on the central charge whereas g depends on the whole operator content.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗