Quark-model relations among TMDs in the parton model
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75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
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Mass gaps of a Z 3 gauge theory with three fermion flavors in 1 + 1 dimensions
We consider a Z 3 gauge theory coupled to three degenerate massive flavors of fermions, which we term Quantum Z(3) Dynamics, QZD. The spectrum can be computed in 1 + 1 dimensions using tensor networks. In weak coupling the spectrum is that of the expected mesons and baryons, although the corrections in weak coupling are nontrivial, analogous to those of nonrelativistic QED in 1 + 1 dimensions. In strong coupling, besides the usual baryon, the singlet meson is a baryon-antibaryon state. For two special values of the coupling constant, the lightest baryon is degenerate with the lightest octet meson, and the lightest singlet meson, respectively. Published by the American Physical Society 2024
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Calorimetric measurement of nuclear spin-lattice relaxation rate in metals
The quasiparticle density of states in correlated and quantum-critical metals directly probes the effect of electronic correlations on the Fermi surface. Measurements of the nuclear spin-lattice relaxation rate provide one such experimental probe of quasiparticle mass through the electronic density of states. By far the most common way of accessing the spin-lattice relaxation rate is via nuclear magnetic resonance and nuclear quadrupole resonance experiments, which require resonant excitation of nuclear spin transitions. Here we report nonresonant access to spin-lattice relaxation dynamics in AC-calorimetric measurements. The nuclear spin-lattice relaxation rate is inferred in our measurements from its effect on the frequency dispersion of the thermal response of the calorimeter-sample assembly. Further, we use fast, lithographically defined nanocalorimeters to access the nuclear spin-lattice relaxation times in metallic indium from 0.3 to 7 K and in magnetic fields up to 35 T.
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First-order phase transition to a nonmagnetic ground state in nonsymmorphic NbCrP
Here, we report the discovery of a first-order phase transition at around 125 K in NbCrP, which is a nonsymmorphic crystal with the P n m a space group. From the resistivity, magnetic susceptibility, and nuclear magnetic resonance measurements using crystals made by the Sn-flux method, the high-temperature (HT) phase is characterized to be metallic with a non-negligible magnetic anisotropy. The low-temperature (LT) phase is also found to be a nonmagnetic metallic state with a crystal of lower symmetry. In the LT phase, the spin susceptibility is reduced by ~30 % from that in the HT phase, suggesting that the phase transition is triggered by the electronic instability. The possible origin of the phase transition in NbCrP is discussed based on the electronic structure by comparing it with those in other nonsymmorphic compounds, RuP and RuAs.
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Measures of complexity and entanglement in many-fermion systems
There is no unique and widely accepted definition of the complexity measure (CM) of a many-fermion wave function in the presence of interactions. The simplest many-fermion wave function is a Slater determinant. In shell-model or configuration interaction (CI) and other related methods, the state is represented as a superposition of a large number of Slater determinants, which in the case of CI calculations reaches about 20 billion terms [Johnson, arXiv:1809.07869]. Although in practice this number has been used as a CM for decades, it is ill defined: it is not unique, and it depends on the particular type and the number of single-particle wave functions used to construct the Slater determinants. Further, the canonical wave functions and/or natural orbitals [Löwdin, Adv. Phys. 5, 1 (1956); Löwdin and Shull, Phys. Rev. 101, 1730 (1956); Bardeen et al., Phys. Rev. 108, 1175 (1957); N. N. Bogoljubov, Il Nuovo Cimento 7, 794 (1958); Valatin, Il Nuovo Cimento 7, 843 (1958); de Gennes, Superconductivity of Metals and Alloys (CRC Press, Boca Raton, FL, 1999); Ring and Schuck, The Nuclear Many-Body Problem, 1st ed. (Springer-Verlag, Berlin, 2004)] and their corresponding occupation probabilities are intrinsic properties of any many-body wave function, irrespective of the representation, and they provide a unique solution to characterize the CM. The non-negative orbital entanglement entropy, which vanishes for a Slater determinant, provides the simplest CM, while a more complete measure of complexity is the entanglement spectrum. We illustrate these aspects in the case of a complex nonequilibrium time-dependent process, induced nuclear fission described within a real-time density functional theory framework extended to superfluid systems, which can describe simultaneously the long-range and the short-range correlations between fermions. The orbital entanglement entropy of the fissioning nucleus illustrates the localization mechanism of the many-body wave function in Fock and/or Hilbert space. The (minimal) number of Slater determinants required to represent such a complex many-body wave function with a well-defined number of particles in the case presented here is about 10 500 . The realistic case of the highly nonequilibrium nuclear fission process illustrated here is equivalent to a system of 23.328×10 9 interacting quantum spin-1/2 particles, a very large system for the study of quantum entanglement.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Mixed ortho- H 2 and para- H 2 clusters studied by vibrational coherent anti-Stokes Raman spectroscopy
The search for macroscopic quantum effects, including superfluidity, in molecular hydrogen is mostly focused on its parahydrogen (p-H 2 ) nuclear spin modification because of weaker intermolecular interaction compared to orthohydrogen (o-H 2 ), both modifications being bosonic. In this work, mixed clusters of o-H 2 and p-H 2 containing similar to 10(4) molecules are prepared by supersonic expansion with helium and studied by vibrational coherent anti-Stokes Raman scattering (CARS) spectroscopy. At similar experimental conditions the neat p-H 2 clusters avoid freezing and remain fluid at 1-2 K, which is predicted to be the realm of their superfluid behavior [Phys. Rev. Lett. 101, 205301 (2008)]. Dependence of the vibrational frequencies and intensities of the main CARS peaks due to o-H 2 and p-H 2 versus the ratio of the o-H 2 and p-H 2 concentrations in the expanding gas suggests that o-H 2 and p-H 2 molecules are uniformly mixed in the interior of the clusters. A weak spectral feature at 4157 cm -1 that appears independent of the concentration ratio is assigned to the outer shell of the clusters enriched with p-H 2 molecules. Although the phase of the mixed clusters could not be unambiguously identified, the shift of the vibrational frequencies with respect to the bulk solid is consistent with the liquid state of the clusters.
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In-Situ Transmission Electron Microscopy Study of the Evolution of Extended Defects in Oxide Nuclear Fuels
In-situ transmission electron microscopy (TEM) with simulated extreme environments is an effective tool for understanding and tracking microstructural changes down to the atomic scale. The objective of this research is to study the effect of temperature on the evolution of extended defects in ThO2 and UO2. Here, we present in-situ TEM isochronal thermal annealing experiments using a micro-electro-mechanical-system (MEMS)-based heating holder. ThO2 and UO2 single crystal specimens were grown inside an inert silver ampoule using hydrothermal synthesis. Both samples were irradiated using 2 MeV protons at 600oC up to 0.1 dpa at Texas A&M University’s Accelerator Laboratory. Fig. 1a shows a weak-beam dark field TEM image of ThO2 after irradiation, indicating the presence of faulted 1/3 <111> type dislocation loops. This presentation will discuss the effect of annealing temperature (600oC, 800oC, 1000oC, 1100oC, etc.) on dislocation loop density, size and distribution, loop nature (interstitial/vacancies) and Burgers vector, as well as the formation of voids in both ThO2 and UO2. This work will also discuss the interaction between defects during annealing. The in-situ TEM annealing cycle is shown in Fig 1b. This research significantly improves the understanding of defect behavior in oxide nuclear fuels with temperature and will aid computational modeling efforts. This work was supported as part of the Center for Thermal Energy Transport under Irradiation (TETI) Energy Frontier Research Center, funded by the U.S. Department of Energy Office of Science.
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Charged Defects in UO 2 Bulk and Surface: A First-Principles Study
Uranium dioxide (UO 2 ) is the primary fuel used in nuclear reactors. Under the extreme heat and radiation inside a reactor, this material inevitably develops defects in its crystal structure. To investigate the nature and behavior of these defects, DFT+U calculations were employed to investigate charged point defects in both bulk UO 2 and its most stable surface, the (111) plane. The formation of defects and their impact on the electronic structure were systematically examined. The results reveal that these defects introduce localized electronic states, alter magnetic behavior, and modify the structural properties. In general, such defects act as deep traps capable of capturing and retaining charge carriers. The stability of these defects depends strongly on the chemical environment and the position of the Fermi level. Surface defect calculations reveal that oxygen vacancies form more readily at the surface than in the bulk over a wide range of electron chemical potential, with subsurface oxygen vacancies being more stable than those in the top layer. Overall, the findings demonstrate how charged defects influence magnetism, transport, and stability in UO 2 , providing insights that may guide improvements in the safety and efficiency of nuclear fuel.
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Science & Technology Review December 2025 - Optimizing Future Design
At Lawrence Livermore National Laboratory, we focus on science and technology research to ensure our nation’s security. We also apply that expertise to solve other important national problems in energy, bioscience, and the environment. Science & Technology Review is published eight times a year to communicate, to a broad audience, the Laboratory’s scientific and technological accomplishments in fulfilling its primary missions. The publication’s goal is to help readers understand these accomplishments and appreciate their value to the individual citizen, the nation, and the world.
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Quantum simulations of SO(5) many-fermion systems using qudits
The structure and dynamics of many-body systems are the result of a delicate interplay between underlying interactions. Fermionic pairing, for example, plays a central role in various physical systems, ranging from condensed matter to nuclear systems, where it can lead to collective phenomena such as superconductivity and superfluidity. In atomic nuclei, the interplay between pairing and particle-hole interactions leads to a high degree of complexity and intricate entanglement structures. Despite this apparent complexity, symmetries emerge and manifest themselves in observable regular patterns. These symmetries and their breakings have long been used to determine relevant degrees of freedom and simplify classical descriptions of many-body systems. Here, this work explores the potential utility of quantum computers with arrays of qudits in simulating interacting fermionic systems, when the qudits can naturally map the relevant degrees of freedom determined by an underlying symmetry group. The Agassi model of fermions interacting via particle-hole and pairing interactions is based on an underlying so(5) algebra. Such systems can intuitively be partitioned into pairs of modes with five basis states, which thus naturally map to arrays of d = 5 qudits (qu5its). Classical noiseless simulations of the time evolution of systems with up to twelve qu5its are performed, by implementing quantum circuits that are developed herein, using PYTHON codes invoking Google's CIRQ software. The resource requirements of the qu5it circuits are analyzed and compared with two different mappings to qubit systems: a physics-aware Jordan-Wigner mapping requiring four qubits per mode pair and a state-to-state mapping requiring three qubits per mode pair. While the dimensionality of Hilbert spaces in mappings to qu5it systems are less than those for the corresponding qubit systems, the number of entangling operations, depending on the available hardware, can either be greater or smaller than for the physics-aware Jordan-Wigner mapping. The state-to-state mapping, while having a smaller Hilbert space than Jordan-Wigner mappings, appears to be the least efficient in gate counts. Further, a previously unknown sign problem has been identified from Trotterization errors in time evolving high-energy excitations. There appear to be advantages in employing quantum computers with arrays of qudits to perform simulations of many-body dynamics that exploit the role of underlying symmetries, specifically in lowering the required quantum resources and in reducing anticipated errors that take the simulation out of the physical space. If the necessary entangling gates are not directly supported by the hardware, physics-aware mappings to qubits may, however, be advantageous for other aspects.
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SPLENDAQ: A Detector-Agnostic Data Acquisition System for Small-Scale Physics Experiments
Many scientific applications from rare-event searches to condensed matter system characterization to high-rate nuclear experiments require time-domain triggering on a raw stream of data, where the triggering is generally threshold-based or randomly acquired. When carrying out detector R &D, there is a need for a general data acquisition (DAQ) system to quickly and efficiently process such data. In the SPLENDOR collaboration, we are developing the Python-based SPLENDAQ package for this exact purpose—it offers two main features for offline analysis of continuous data: a threshold triggering algorithm based on the time-domain optimal filter formalism and an algorithm for randomly choosing nonoverlapping segments for noise measurements. Further, combined with the commercially available Moku platform, developed by Liquid Instruments, we have a full pipeline of event building off raw data with minimal setup. Here, we review the underlying principles of this detector-agnostic DAQ package and give concrete examples of its utility in various applications.
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Lattice anharmonicity effects in fluorite oxide single crystals and anomalous increase in phonon lifetime in ceria at elevated temperature
Here, we investigate the temperature dependence of the frequency and linewidth of the triply degenerate T 2g zone-centered optical phonon in flux-grown ceria and hydrothermally synthesized thoria single crystals from room temperature to 1273 K using Raman spectroscopy. Both crystals exhibit an expected increase in the phonon linewidth with temperature due to enhanced phonon–phonon scattering. However, ceria displays an anomalous linewidth reduction in the temperature range of 1023–1123 K. First-principles phonon linewidth calculations considering cubic and quartic phonon interactions within temperature-independent phonon dispersion fail to describe this anomaly. A parameterization of the temperature-dependent second-order interatomic force constants based on previously reported phonon dispersion measured at room and high temperatures predicts a deviation from the monotonic linewidth increase, albeit at temperatures lower than those observed experimentally for ceria. The qualitative agreement in the trend of temperature-dependent linewidth suggests that lattice anharmonicity-induced phonon renormalization plays a role in phonon lifetime. Specifically, a change in the overlap between softened acoustic and optical branches in the dispersion curve reduces the available phonon scattering phase space of the Raman-active mode at the zone center, leading to an increased phonon lifetime within a narrow temperature interval. These findings provide insights into higher-order anharmonic interactions in ceria and thoria, motivating further investigations into the role of anharmonicity-induced phonon renormalization on phonon lifetimes at high temperatures.
11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Effects of Na deficiency on spin dynamics in the Mott insulating Na 4−x Ir 3 O 8
Here, we report on Raman scattering and 23 Na nuclear magnetic resonance (NMR) investigations of j eff = 1/2 hyperkagome antiferromagnet Na 4−x Ir 3 O 8 , which lies in the Mott insulating state. Our Raman scattering experiments unveil remarkable parallels between the magnetic excitations of the pristine Na 4 Ir 3 O 8 and the Kitaev honeycomb material Na 2 IrO 3 , which are characterized by dominant fractional spinon excitations. In the case of moderate Na-deficient Na 4−x Ir 3 O 8 , however, a substantial suppression of the magnetic excitations is observed, alluding to the notable influence of charge fluctuations on spin dynamics. In addition, our site-specific 23 Na NMR measurements offer further insights into the spin dynamics when a minor concentration of holes is introduced into a spin-orbit coupled Mott insulator. Specifically, the spin-lattice relaxation rate 1/ T 1 reveals the emergence of pseudogaplike correlations at the Na(2) site, alongside a critical slowing down behavior at the Na(1) and Na(3) sites. These findings showcase the intricate interplay between itinerant holes and magnetic correlations in a spin-liquid-like background.
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Interrelationships between nematicity, antiferromagnetic spin fluctuations, and superconductivity: Role of hotspots in FeSe 1 - x S x revealed by high pressure Se 77 NMR study
The sulfur-substituted FeSe, FeSe 1-x S x , is one of the unique systems that provides an independent tunability of nematicity, antiferromagnetism, and superconductivity under pressure (p). Recently, Rana et al. [K. Rana et al., Phys. Rev. B 101, 180503(R) (2020)] reported, from 77 Se nuclear magnetic resonance (NMR) measurements on FeSe 0.91 S 0.09 under pressure, that there exists a clear role of nematicity in the relationship between antiferromagnetic (AFM) spin fluctuations and the superconducting transition temperature (T c ), where the AFM spin fluctuations are more effective in enhancing T c in the absence of nematicity than with nematicity. Here, motivated by the work, we carried out 77 Se NMR measurements on FeSe 1-x S x with x=0.15 and 0.29 under pressure up to 2.10 GPa to investigate the relationship in a wide range of x in the FeSe 1-x S x system. Based on the new results together with the previously reported data for x=0 [P. Wiecki et al., Phys. Rev. B 96, 180502(R) (2017)] and 0.09 [K. Rana et al. Phys. Rev. B 101, 180503(R) (2020)], we established a p–x–temperature (T) phase diagram exhibiting the evolution of AFM spin fluctuations. From the systematic analysis of the NMR data, we found that the superconducting (SC) state in a nematic state arises from a non-Fermi-liquid state with strong stripe-type AFM spin fluctuations, while the SC state without nematicity comes from a Fermi-liquid state with mild stripe-type AFM spin fluctuations. Furthermore, we show that the previously reported impact of nematicity on the relationship between AFM fluctuations and superconductivity holds throughout the wide range of x from x=0 to 0.29 in FeSe 1-x S x under pressure. We discuss the origin of the role of nematicity in terms of the different numbers of hotspots on Fermi surfaces with and without nematicity.
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Itinerant G-type antiferromagnet SrCr 2 As 2 studied by magnetization, heat capacity, electrical resistivity, and NMR measurements
Here, the physical properties of itinerant antiferromagnetic (AFM) SrCr 2 As 2 with body-centered tetragonal ThCr 2 Si 2 structure were investigated in single crystalline and polycrystalline forms by electrical resistivity ρ, heat capacity C p , magnetic susceptibility χ versus temperature T, and magnetization M versus applied magnetic field H isotherm measurements as well as 75 As and 53 Cr nuclear magnetic resonance (NMR) measurements in the wide temperature range T = 1.6–900 K. From the χ(T) and 75 As NMR measurements, the G-type AFM state below T N = 615(15) K has been determined, consistent with the previous neutron-diffraction measurements. Direct evidence of magnetic ordering of the Cr spins was shown by the observation of the 53 Cr NMR spectrum under H = 0. From the χ( T) measurements on single-crystal SrCr 2 As 2 under the two different magnetic field directions H|| ab and H || c in the AFM state, the Cr ordered moments are shown to align along the c axis in the G-type AFM state. The metallic state is directly evidenced by the ρ, C p , and NMR measurements, and the density of states at the Fermi energy $\mathscr{D}$(E F ) in the AFM state is estimated to be 7.53 states/eV f.u. for both spin directions which is almost twice the bare $\mathscr{D}$(E F ) estimated from first-principles calculations, suggesting an enhancement of the conduction-carrier mass by a factor of two in the AFM state. The $\mathscr{D}$(E F ) is found to be nearly constant below at least 100 K and is independent of H. The ρ(T) is found to show T-linear behavior above T N and exhibits positive curvature below T N where significant loss of spin-disorder scattering upon magnetic ordering is observed. The resistivity anisotropy of the compound remains moderate ρ c /ρ a ~ 9 through most of the magnetically ordered phase but shows a rapid increase below 50 K.
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Magnetars and axion-like particles: probes with the hard X-ray spectrum
Quiescent hard X-ray and soft gamma-ray emission from neutron stars constitute a promising frontier to explore axion-like-particles (ALPs). ALP production in the core peaks at energies of a few keV to a few hundreds of keV; subsequently, the ALPs escape and convert to photons in the magnetosphere. The emissivity goes as ~T 6 while the conversion probability is enhanced for large magnetic fields, making magnetars, with their high core temperatures and strong magnetic fields, ideal targets for probing ALPs. We compute the energy spectrum of photons resulting from conversion of ALPs in the magnetosphere and then compare it against hard X-ray data from NuSTAR, INTEGRAL, and XMM-Newton, for a set of eight magnetars for which such data exists. Upper limits are placed on the product of the ALP-nucleon and ALP-photon couplings. For the production in the core, we perform a calculation of the ALP emissivity in degenerate nuclear matter modeled by a relativistic mean field theory. The reduction of the emissivity due to improvements to the one-pion exchange approximation is incorporated, as is the suppression of the emissivity due to proton superfluidity in the neutron star core. A range of core temperatures is considered, corresponding to different models of the steady heat transfer from the core to the stellar surface. For the subsequent conversion, we solve the coupled differential equations mixing ALPs and photons in the magnetosphere. The conversion occurs due to a competition between the dipolar magnetic field and the photon refractive index induced by the external magnetic field. Semi-analytic expressions are provided alongside the full numerical results. Furthermore, we also present an analysis of the uncertainty on the axion limits we derive due to the uncertainties in the magnetar masses, nuclear matter equation of state, and the proton superfluid critical temperature.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Possible coexistence of antiferromagnetic and ferromagnetic spin fluctuations in the spin-triplet superconductor UTe 2 revealed by 125 Te NMR under pressure
We report a spin-triplet superconducting state mediated by ferromagnetic (FM) spin fluctuations has been suggested to occur in the newly discovered heavy-fermion superconductor UTe 2 . However, the recent neutron scattering measurements revealed the presence of antiferromagnetic (AFM) spin fluctuations in UTe 2 . Here, we report the 125 Te nuclear magnetic resonance studies of a single-crystal UTe 2 , suggesting the coexistence of FM and AFM spin fluctuations in UTe 2 . Owing to the two different Te sites in the compound, we conclude that the FM spin fluctuations are dominant within ladders and the AFM spin fluctuations originate from the interladder magnetic coupling. Although AFM spin fluctuations exist in the system, the FM spin fluctuations in the ladders may play an important role in the appearance of the spin-triplet superconducting state of UTe 2 .
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Astrophysical Equation-of-State Constraints on the Color-Superconducting Gap
We demonstrate that astrophysical constraints on the dense-matter equation of state place an upper bound on the color-superconducting gap in dense matter above the transition from nuclear matter to quark matter. Pairing effects in the color-flavor locked quark matter phase increase the pressure at high density, and if this effect is sufficiently large then the requirements of causality and mechanical stability make it impossible to reach such a pressure in a way that is consistent with what is known at lower densities. The intermediate-density equation of state is inferred by considering extensions of chiral effective field theory to neutron star densities, and conditioning these using current astrophysical observations of neutron star radius, maximum mass, and tidal deformability (PSR J0348+0432, PSR J1624-2230, PSR J0740+6620, GW170817). At baryon number chemical potential μ = 2.6 GeV we find a 95% upper limit on the color-flavor locked pairing gap Δ of 457 MeV using overly conservative assumptions and 216 MeV with more reasonable assumptions. Furthermore, this constraint may be strengthened by future astrophysical measurements as well as by future advances in high-density QCD calculations.
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