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63 records · Page 4

Smooth splitting and zeros from on-shell recursion

We describe a new approach to understanding the origins of recently discovered “hidden zeros” and “smooth splitting” of tree-level amplitudes in Tr ϕ 3 , Non-Linear Sigma Model (NLSM), Yang-Mill-Scalar (YMS) and the special Galileon. Introducing a new type of linear shift in kinematic space we demonstrate that the mysterious splitting formulae follow from a simple contour integration argument in the style of on-shell recursion. The argument makes use of only standard notions of tree-level factorization on propagators, but assumes improved UV behavior in the form of the absence of a residue at infinity. In the case of Tr ϕ 3 and NLSM this is proven by identifying our shift as a special case of a more general construction called a g-vector shift; in the case of YMS it remains an unproven conjecture. This recursive perspective leads to numerous new results: we derive generalizations of the splitting formulae on more relaxed near-zero kinematics, including interesting new kinematic limits in which the amplitude splits into a triple-product; we also demonstrate that the uncolored special Galileon model has improved UV scaling and hence also splits. We also investigate the possible realization of hidden zeros in four dimensions. The conditions under which the dimensionality constraints are compatible with zero kinematics is investigated in detail for Tr ϕ 3 and YMS; for the latter we find they can be realized only with certain restrictions on external helicity states. The realizable 4d zeros are proven by a similar recursive argument based on BCFW and is found to generalize to a new class of intrinsically 4d “helicity zeros” present in all sectors of YM and also gravity.

effective field theories↗

Hidden zeros of the cosmological wavefunction

Motivated by the recent discovery of hidden zeros in particle and string amplitudes, we characterize zeros of individual graph contributions to the cosmological wavefunction of a scalar field theory. We demonstrate that these contributions factorize near these zeros for all tree graphs and provide evidence that this extends to loop graphs as well. We explicitly construct polytopal realizations of the relevant graph associahedra and show that the cosmological zeros have natural geometric and physical interpretations. As a byproduct, we establish an equivalence between the wavefunction coefficients of chain graphs and flat-space Tr(ϕ 3 ) amplitudes, enabling us to leverage the cosmological zeros to uncover the recently discovered hidden zeros of colored amplitudes.

Cosmological models↗

Frustration-driven magnetic correlations in the spin-$\frac{5}{2}$ triangular lattice antiferromagnet RbFe⁢(HPO 3 ) 2

Here, a detailed study of the structural and magnetic properties of a spin-5/2 triangular lattice antiferromagnet RbFe⁢(HPO 3 ) 2 is presented using x-ray diffraction, magnetization, heat capacity, and 31 P nuclear magnetic resonance (NMR) experiments on a polycrystalline sample. The crystal structure features an equilateral triangular lattice of Fe 3+ ions. The thermodynamic measurements reveal the onset of a magnetic long-range order at 𝑇 N⁢1 ≃7.8K in zero field, followed by another low-temperature field-induced ordering at 𝑇 N⁢2 in higher fields. The transition at 𝑇 N⁢1 is further confirmed from the NMR spin lattice relaxation measurements. The value of the frustration ratio (𝑓≃7) implies moderate spin frustration in the compound. The 31 P NMR spectra exhibit two distinct spectral lines corresponding to two inequivalent phosphorus sites (P1 and P2), consistent with the crystal structure. The P1 site is strongly coupled with an isotropic hyperfine coupling of 𝐴$^{iso}_{hf}$ = 0.55⁢(2)⁢ T/𝜇 B while the P2 site is weakly coupled with 𝐴$^{iso}_{hf}$ = 0.25⁢(3)⁢ T/𝜇 B with the Fe 3+ ions. The magnetic susceptibility and NMR shift data are described well assuming a spin-5/2 isotropic triangular lattice antiferromagnetic model with an average exchange coupling of 𝐽/𝑘 B = 2.8⁢(2)⁢K. Below 𝑇 N⁢1 , the spectra evolve into a nearly rectangular powder pattern, indicating a commensurate antiferromagnetic type order. The 31 P spin-lattice relaxation rate well below 𝑇N⁢1 follows a 𝑇 3 temperature dependence, implying a two-magnon Raman scattering mechanism in the ordered state. Three well-defined phase regimes are clearly ascertained in the 𝐻−𝑇 phase diagram, reflecting a weak magnetic anisotropy in the compound.

Nagpal, V. [Indian Institute of Science Education ↗

Noncollinear polar magnet Fe 2 (SeO 3 ) 3 (H 2 O) 3 with inequivalent Fe 3+ sites

The emergence of novel magnetic states becomes more likely when the inversion symmetry of the crystal field, relative to the center between two spins, is broken. We propose that placing magnetic spins in inequivalent sites in a polar lattice can promote a realization of nontrivial magnetic states and associated magnetic properties. To test our hypothesis, we study Fe 2 (SeO 3 )(H 2 O) 3 as a model system that displays two distinct Fe(1) and Fe(2) magnetic sites in a polar structure (R3c space group). At low fields μ 0 H≤ 0.06 T, the material undergoes an antiferromagnetic ordering with T N1 = 77 K and a second transition at T N2 ≈ 4 K. At μ 0 H≥ 0.06 T and 74 K ≤T≤ 76 K, a positive entropy change of ∼0.12 mJ mol −1 K −1 can be associated with a metamagnetic transition to possibly nontrivial spin states. At zero field, Fe(1) is nearly fully ordered at T≈ 25 K, while Fe(2) features magnetic frustration down to T = 4 K. The magnetic ground state, a result corroborated by single-crystal neutron diffraction and 57 Fe Mössbauer spectroscopy, is a noncollinear antiparallel arrangement of ferrimagnetic Fe(1)–Fe(2) dimers along the c-axis. The results demonstrate that placing distinct magnetic sites in a polar crystal lattice can enable a new pathway to modifying spin, orbital, and lattice degrees of freedom for unconventional magnetism.

Crystal lattices↗

Randomized Algorithms for Scientific Computing (RASC)

Randomized algorithms have propelled advances in artificial intelligence (AI) and represent a foundational research area in advancing AI for Science. Future advancements in DOE Office of Science priority areas such as climate science, astrophysics, fusion, advanced materials, combustion, and quantum computing all require randomized algorithms for surmounting challenges of complexity, robustness, and scalability. Advances in data collection and numerical simulation have changed the dynamics of scientific research and motivate the need for randomized algorithms. For instance, advances in imaging technologies such as X-ray ptychography, electron microscopy, electron energy loss spectroscopy, or adaptive optics lattice light-sheet microscopy collect hyperspectral imaging and scattering data in terabytes, at breakneck speed enabled by state-of-the-art detectors. The data collection is exceptionally fast compared with its analysis. Likewise, advances in high-performance architectures have made exascale computing a reality and changed the economies of scientific computing in the process. Floating-point operations that create data are essentially free in comparison with data movement. Thus far, most approaches have focused on creating faster hardware. Ironically, this faster hardware has exacerbated the problem by making data still easier to create. Under such an onslaught, scientists often resort to heuristic deterministic sampling schemes (e.g., low-precision arithmetic, sampling every nth element) and sacrifice potentially valuable accuracy. Dramatically better results can be achieved via randomized algorithms, reducing the data size as much as or more than naive deterministic subsampling can achieve, while retaining the high accuracy of computing on the full data set. By randomized algorithms we mean those algorithms that employ some form of randomness in internal algorithmic decisions to accelerate time to solution, increase scalability, or improve reliability. Examples include matrix sketching for solving large-scale least-squares problems (see Figure 1) and stochastic gradient descent for training machine learning models. We are not recommending heuristic methods but rather randomized algorithms that have certificates of correctness and probabilistic guarantees of optimality and near-optimality. Such approaches can be useful beyond acceleration, for example, in understanding how to avoid measure zero worst-case scenarios that plague methods such as QR matrix factorization.

97 MATHEMATICS AND COMPUTING↗

Characterizing the surface compositions of supported bimetallic PtSn clusters: Effects of cluster-support interactions and surface adsorbates

PtSn bimetallic clusters on TiO2(110) and highly oriented pyrolytic graphite (HOPG) surfaces have been characterized by scanning tunneling microscopy, low energy ion scattering (LEIS), Xray photoelectron spectroscopy, and temperature programmed desorption (TPD); density functional theory (DFT) calculations have also been performed to better understand adsorption of CO and D2 on the PtSn surfaces. On TiO2 at coverages of 2 ML of Pt and 2 ML of Sn, exclusively bimetallic clusters are formed for both orders of deposition because clusters of the first metal completely cover the surface such that all atoms of the second metal are incorporated into the existing clusters. In contrast, on HOPG, the high mobility and weak cluster-support interactions on HOPG result in much larger 2 ML monometallic clusters (~30 Å high) that do not completely cover the surface, and deposition of the second metal produces larger clusters as well as smaller ones. Despite the difference in cluster morphologies for the different orders of deposition and supports, the LEIS experiments demonstrate that in all cases, the PtSn clusters are rich in Sn at the surface, as expected based on the lower surface free energy for Sn compared to Pt. Furthermore, the +0.2 eV shift in the Sn(3d5/2) binding energy observed on all surfaces in the presence of Pt is consistent with PtSn alloy formation. Deposition of 2 ML of Sn on TiO2 produces two-dimensional clusters with oxidation of Sn and reduction of titania at the clustersupport interface, but addition of Pt to the Sn clusters causes Sn to diffuse away from this interface, leaving Sn in the metallic state. TPD experiments on 2 ML Pt/TiO2 with increasing coverages of Sn show that the number of adsorption sites for D2 sharply decreases to nearly zero at 0.5 ML, while CO adsorption decreases to zero only at much higher Sn coverages of 2 ML. DFT studies for Sn modified Pt surfaces and bulk structures demonstrate that for CO adsorption at low Sn coverages (<0.25 ML), the strong Pt-CO interactions induce diffusion of Pt to the cluster surface and the formation of a bulk Pt3Sn alloy, whereas D2 adsorption does not lead to interactions with the Pt surface that are strong enough to induce alloy formation. A single Sn adatom prevents D2 adsorption on four neighboring Pt atoms via site-blocking and the donation of electron density to Pt.

Li, Fangliang↗

Equilibrium Fe isotope fractionation between olivine, pyroxene, spinel and MORB glass: Implications for mantle partial melting to generate MORBs

Primitive mid-ocean ridge basalts (MORBs) exhibit Fe isotopic compositions heavier than the upper mantle by +0.074 ± 0.028 ‰ for δ 56 Fe. The processes responsible for this isotopic difference remain unclear. Modeling of Fe isotope fractionation during mantle partial melting requires reliable equilibrium Fe isotope fractionation factors between minerals and melts, for which consistent data are still lacking. Here, in this study, we used Nuclear Resonant Inelastic X-ray Scattering (NRIXS) technique to measure Fe force constants for a MORB glass (ALV 519-4-1) and natural mantle minerals (olivine, orthopyroxene, clinopyroxene, and spinel) to determine the equilibrium Fe isotope fractionation factors between them. The force constants determined in this study, in increasing order, are 167 ± 26 N/m for spinel, 175 ± 17 N/m for olivine, 176 ± 20 N/m for MORB glass, 205 ± 26 N/m for clinopyroxene, and 219 ± 36 N/m for orthopyroxene. We evaluated the previously proposed mechanisms for the heavy Fe isotopic composition of MORBs, including (i) mantle partial melting, (ii) mantle lithological heterogeneity, with pyroxenite in the source, (iii) mantle metasomatism by low-degree melts, and (iv) fractional crystallization of olivine from melts. For (i), we used the pMELTS program to simulate adiabatic decompression melting of mantle peridotites, and calculated Fe isotope fractionation based on Fe 3+ –Fe 2+ equilibrium-controlled fractionation, where Fe 3+ forms stronger bonds and is more incompatible than Fe 2+ . At 10 wt% peridotite melting, corresponding to MORB generation, only +0.03 ‰ Fe isotope fractionation between the melt and the original bulk composition (Δ 56 Fe = δ 56 Fe melt - δ 56 Fe 0 ) was produced, insufficient to account for the observed MORB-upper mantle difference. For (ii), melting of pyroxenites yields smaller Fe isotope fractionation than melting of peridotites, making it unlikely the cause for the MORB-upper mantle isotopic difference. For (iii), both the Fe 3+ /ΣFe ratio and the δ 56 Fe of melts increase with the degree of partial melting, indicating that low-degree melts are not isotopically heavy enough to significantly alter the isotopic composition of lithospheric mantle through metasomatism. For (iv), equilibrium isotope fractionation between olivine and melt is near zero. These results suggest that equilibrium Fe isotope fractionation alone cannot explain the MORB isotopic signature, highlighting the potential role of kinetic isotope fractionation. Using a diffusion model, we calculated kinetic Fe and Mg isotope fractionations associated with (iv) olivine crystallization from a melt, and found that the predicted Fe and Mg isotope fractionations were inconsistent with observations in MORBs. Qualitatively, two processes could have induced kinetic Fe isotope fractionation during MORB generation: (a) Fe-Mg interdiffusion between melt and solid during melt migration and (b) reactive melt-rock interactions during melt focusing. However, a quantitative understanding of their role in modifying the melt isotopic composition remains limited and requires further investigation.

Fe isotopes↗

Anisotropic magnetism and electronic structure of trigonal EuAl 2 Ge 2 single crystals

Understanding the interplay between magnetic and electronic degrees of freedom is of profound recent interest in different Eu-based magnetic topological materials. Here, we studied the magnetic and electronic properties of the layered Zintl-phase compound EuAl 2 Ge 2 crystallizing in the trigonal CaAl 2 Si 2 -type structure. We report zero-field neutron diffraction, temperature T - and magnetic-field H-dependent magnetic susceptibility χ(T, H), isothermal magnetization M(T, H), heat capacity C p (T, H), and electrical resistivity ρ(T, H) measurements, together with T-dependent angle-resolved photoemission spectroscopy (ARPES) measurements complemented with first-principle calculations. EuAl 2 Ge 2 undergoes second-order A-type antiferromagnetic (AFM) ordering below T N = 27.5(5) K, with the Eu moments (Eu 2+ , S = 7/2) aligned ferromagnetically in the ab plane while these layers are stacked antiferromagnetically along the c axis. The critical fields at which all moments become parallel to the field are 37.5(5) and 52.5(5) kOe for H ∥ ab and H ∥ c, respectively. The H = 0 magnetic structure consists of trigonal AFM domains associated with ab-plane magnetic anisotropy and a field-induced reorientation of the Eu spins in the domains is also evident at T = 2 K below the critical field H c1 = 2.5(1) kOe. The ρ(T) measurements reveal metallic behavior transforming into a slight resistivity increase on cooling towards T N . A pronounced loss of spin-disorder scattering is observed below T N . The ARPES results show that EuAl 2 Ge 2 is metallic both above and below T N , and the Fermi surface is anisotropic with two hole pockets at the zone center and one small electron pocket at each M point. In the AFM phase, we directly observe folded bands in ARPES due to the doubling of the magnetic unit cell along the c axis with an enhancement of quasiparticle weight due to the complex change in the coupling between the magnetic moments and itinerant electrons on cooling below T N . The observed electronic structure is well reproduced by first-principle calculations, which also predict the presence of nontrivial electronic states near the Fermi level in the AFM phase with Z 2 topological numbers 1;(000)

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗