Large Symmetry Research Articles

Diamond of infrared equivalences in abelian gauge theories

We demonstrate a tree-level equivalence between four distinct infrared objects in (d+2)-dimensional Abelian gauge theories. These are (i) the large gauge charge Qϵ where the function ϵ on the sphere parametrizing large gauge transformations is identified with the Goldstone mode θ of spontaneously broken large gauge symmetry; (ii) the soft effective action that captures the dynamics of the soft and Goldstone modes; (iii) the edge mode action with Neumann boundary conditions; and (iv) the Wilson line dressing of a scattering amplitude, including a novel dressing for soft photons, which have local charge distributions despite having vanishing global charge. The promotion of the large gauge parameter to the dynamical Goldstone and the novel dressing of soft gauge particles give rise to intriguing possibilities for the future study of infrared dynamics of gauge theories and gravity. Published by the American Physical Society 2024

Dynamics of vortex cap solutions on the rotating unit sphere

In this work, we analytically study the existence of periodic vortex cap solutions for the homogeneous and incompressible Euler equations on the rotating unit 2-sphere, which was numerically conjectured in [28,29,60,61]. Such solutions are piecewise constant vorticity distributions, subject to the Gauss constraint and rotating uniformly around the vertical axis. The proof is based on the bifurcation from zonal solutions given by spherical caps. For the one–interface case, the bifurcation eigenvalues correspond to Burbea's frequencies obtained in the planar case but shifted by the rotation speed of the sphere. The two–interfaces case (also called band type or strip type solutions) is more delicate. Though, for any fixed large enough symmetry, and under some non-degeneracy conditions to avoid spectral collisions, we achieve the existence of at most two branches of bifurcation.

Understanding small neutrino mass and its implication

We have derived previously the relations between the neutrino masses and mixing angles in a dispersive analysis on the mixing of neutral leptonic states. The only involved assumption is that the electroweak symmetry of the Standard Model (SM) is restored at a high energy scale in some new physics scenario, which diminishes the box diagrams responsible for the mixing. Here we include corrections to the analysis up to three loops, arising from exchanges of additional neutral and charged scalars in the electroweak symmetric phase. The solution to the dispersion relation for the μ−e+-μ+e− mixing generates a typical neutrino mass mν∼O(1)eV in the SM unambiguously. The solution also favors the normal ordering of the neutrino masses over the inverted one, and links the large electroweak symmetry restoration, i.e., new physics scale to the small neutrino mass.

Nc -insensitivity of QCD2A

The spectrum of two-dimensional adjoint QCD is surprisingly insensitive to the number of colors Nc of its gauge group. It is argued that the cancellation of finite Nc terms is rather natural and ultimately a consequence of the singularity structure of the theory. In short, there are no finite Nc terms, hence effectively there cannot be any finite Nc singular terms, since the former are necessary to guarantee well-behaved principal value integrals. We evaluate and categorize the matrix elements of the theory’s light-cone Hamiltonian to show how terms emerging from finite Nc contributions to the anticommutator cancel against contributions from the purely finite Nc term of the Hamiltonian. The cancellation is not complete; finite terms survive and modify the spectrum, as is known from numerical work. Additionally we show that several parton-number changing finite Nc matrix elements vanish independently of finiteness requirements. In particular, there is only one trace-diagonal finite Nc correction. It seems therefore that considering matrix elements rather than individual contributions can provide substantial simplifications when computing the spectrum of a theory with a large symmetry group. Published by the American Physical Society 2024

Hierarchy of emergent cluster states by measurement from symmetry-protected-topological states with large symmetry to a subsystem cat state

Hierarchy of emergent cluster states by measurement from symmetry-protected-topological states with large symmetry to a subsystem cat state

Quench dynamics in lattices above one dimension: The free fermionic case

We begin a systematic investigation of quench dynamics in higher-dimensional lattice systems considering the case of noninteracting fermions with conserved particle number. We prepare the system in a translational-invariant nonequilibrium initial state, the simplest example being a classical configuration with fermions at fixed positions on the lattice, and let it evolve in time. We characterize the system's dynamics by measuring the entanglement between a finite connected region and its complement. We observe the transmutation of entanglement entropy into thermodynamic entropy and investigate how this process depends on the shape and orientation of the region with respect to the underlying lattice. Interestingly, we find that irregular regions display a distinctive multislope entanglement growth, while the dependence on the orientation angle is generically fairly weak. This is particularly true for regions with a large (discrete) rotational symmetry group. The main tool of our analysis is the celebrated quasiparticle picture of Calabrese and Cardy, which we generalize to describe the case at hand. Specifically, we show that for generic initial configurations (even when restricting to classical ones) one has to allow for the production of multiplets involving n>2 quasiparticles and carrying nondiagonal correlations. We obtain quantitatively accurate predictions, tested against exact numerics, and propose an efficient Monte Carlo based scheme to evaluate them for arbitrary connected regions of generic higher-dimensional lattices. Published by the American Physical Society 2024

Quantification of shape parameters of Co-Cr-Mo-Si multiphase compounds and their role in the processing of metal injection molding feedstocks

Particle shape is one of the most important powder attributes affecting the properties of multiphase compounds intended for metal injection molding. This work reports the processability of gas (GA) and water (WA) atomized Co-Cr-Mo-Si alloy related to quantitative analyses of particle shape using a newly developed algorithm based on the Euclidean distance mapping, which results are compared with those of commercially available dynamic image analysis. Both methods reveal similar values for the parameters that quantify the shape of the powders, such as circularity, aspect ratio, and symmetry. The alloys were mixed with wax/high-density polyethylene (50/50 wt%) binder using a double sigma mixer to produce homogeneous feedstocks. The critical solid loading and flow performance corresponding to the differences in powder shapes were derived from the torque and capillary rheometers, respectively, to obtain the optimum molding parameters. A stable and repeatable viscosity was observed for the GA feedstock, whereas the compound containing WA was prone to phase separation during flow. The defect-free sintered specimens were examined by metallographic analysis; the GA powder compound could be sintered to a maximum of 99.2 % of the theoretical density, whereas the irregular WA powder reached a maximum of 98.8 % of the theoretical density, and the carbon residue was found to be higher for the GA feedstock. The GA samples had a significantly higher ultimate tensile strength owing to their larger symmetry, which resulted in a lower porosity and stress concentration.

Light Quark Matter Nuggets, Strangelets and Compact Dwarfs

Light quark matter (i.e., udQM) comprised of up and down quarks might be stable with respect to nuclear matter and strange quark matter (SQM). In this work we investigate the stability of nuggets made of such types of matter, which shows that udQM nuggets at certain sizes are more stable than others if a large symmetry energy is adopted. In such cases, there may be compact dwarfs comprised entirely of udQM nuggets and electrons, i.e., udQM dwarfs. We then examine the structure of such udQM dwarfs and consider their possibility of being covered by normal matter crusts. It is found that udQM dwarfs typically have smaller radii, and those covered by normal matter can explain the recently observed white dwarfs with unusually small radii.

Quasi van der Waals Epitaxy of Single Crystalline GaN on Amorphous SiO2/Si(100) for Monolithic Optoelectronic Integration.

The realization of high quality (0001) GaN on Si(100) is paramount importance for the monolithic integration of Si-based integrated circuits and GaN-enabled optoelectronic devices. Nevertheless, thorny issues including large thermal mismatch and distinct crystal symmetries typically bring about uncontrollable polycrystalline GaN formation with considerable surface roughness on standard Si(100). Here a breakthrough of high-quality single-crystalline GaN film on polycrystalline SiO2/Si(100) is presented by quasi van der Waals epitaxy and fabricate the monolithically integrated photonic chips. The in-plane orientation of epilayer is aligned throughout a slip and rotation of high density AlN nuclei due to weak interfacial forces, while the out-of-plane orientation of GaN can be guided by multi-step growth on transfer-free graphene. For the first time, the monolithic integration of light-emitting diode (LED) and photodetector (PD) devices are accomplished on CMOS-compatible SiO2/Si(100). Remarkably, the self-powered PD affords a rapid response below 250µs under adjacent LED radiation, demonstrating the responsivity and detectivity of 2.01×105 A/W and 4.64×1013Jones, respectively. This work breaks a bottleneck of synthesizing large area single-crystal GaN on Si(100), which is anticipated to motivate the disruptive developments in Si-integrated optoelectronic devices.

Observation of band gap bowing effect vanishing in graded-composition monolayer Mo1−xWxS2 alloy

Over the past decade, tremendous effort has been put into developing 2D semiconductor materials with a tunable bandgap by alloying different individual components. However, the bandgap bowing effect has hindered the ability to arbitrary control the emission of these alloys. In this study, we report the chemical vapor deposition growth of a graded-composition Mo1−xWxS2 monolayer alloy, in which the photoluminescence emission energy exhibits nearly linear variation in the bandgap, indicating the vanishing of the bandgap bowing effect. Polarized Raman measurements show that the polarization is composition dependent, and a large symmetry breaking occurs at the point where the bandgap bowing effect vanishes. This suggests that the vanishing of the bowing effect may be attributed to the symmetry breaking induced by compressive strain. Our findings demonstrate a significant advancement in the synthesis of alloys for future use.

Renormalized electric and magnetic charges for O(rn) large gauge symmetries

In this work we present the construction of a renormalized symplectic form on an extended phases space where the higher order large gauge transformations (LGT) act canonically. The expressions of the subn-leading electric charges associated with each O(rn) LGT are then obtained, in agreement with the expressions previously proposed in [1] by means of the tree-level subn-leading formulas. We also present the duality extension of the extended phase space, computing the full electromagnetic charge algebra, showing a tower of central extensions.

Efficient first-principles electronic transport approach to complex band structure materials: the case of n-type Mg3Sb2

We present an efficient method for accurately computing electronic scattering rates and transport properties in materials with complex band structures. Using ab initio simulations, we calculate a limited number of electron–phonon matrix elements, and extract scattering rates for acoustic and optical processes based on deformation potential theory. Polar optical phonon scattering rates are determined using the Fröhlich model, and ionized impurity scattering rates are derived from the Brooks-Herring theory. Subsequently, electronic transport coefficients are computed within the Boltzmann transport theory. We exemplify our approach with n-type Mg3Sb2, a promising thermoelectric material with a challenging large unit cell and low symmetry. Notably, our method attains competitive accuracy, requiring less than 10% of the computational cost compared to state-of-the-art ab initio methods, dropping to 1% for simpler materials. Additionally, our approach provides explicit information on individual scattering processes, offering an alternative that combines efficiency, robustness, and flexibility beyond the commonly employed constant relaxation time approximation with the accuracy of fully first-principles calculations.

Large isospin symmetry violation in kaon production?

The recent measurements of kaon production in Ar+Sc collisions at 75A GeV/c (√SNN = 11.94 GeV) performed by NA61/SHINE at the CERN SPS resulted in determining the ratio of charged to neutral kaons to be 1.26 ± 0.06. The result, well above unity, cannot be explained by models accounting for known isospin symmetry violating processes. This contribution will present the experimental details of this intriguing result. It will also compare it to the world data on charged to neutral kaon ratio in nucleus-nucleus collisions.

Internal symmetry in Poincarè gauge gravity

We find a large internal symmetry within 4-dimensional Poincarè gauge theory.In the Riemann-Cartan geometry of Poincaré gauge theory the field equation and geodesics are invariant under projective transformation, just as in affine geometry. However, in the Riemann-Cartan case the torsion and nonmetricity tensors change. By generalizing the Riemann-Cartan geometry to allow both torsion and nonmetricity while maintaining local Lorentz symmetry the difference of the antisymmetric part of the nonmetricity Q and the torsion T is a projectively invariant linear combination S = T - Q with the same symmetry as torsion. The structure equations may be written entirely in terms of S and the corresponding Riemann-Cartan curvature. The new description of the geometry has manifest projective and Lorentz symmetries, and vanishing nonmetricity.Torsion, S and Q lie in the vector space of vector-valued 2-forms. Within the extended geometry we define rotations with axis in the direction of S. These rotate both torsion and nonmetricity while leaving S invariant. In n dimensions and (p, q) signature this gives a large internal symmetry. The four dimensional case acquires SO(11,9) or Spin(11,9) internal symmetry, sufficient for the Standard Model.The most general action up to linearity in second derivatives of the solder form includes combinations quadratic in torsion and nonmetricity, torsion-nonmetricity couplings, and the Einstein-Hilbert action. Imposing projective invariance reduces this to dependence on S and curvature alone. The new internal symmetry decouples from gravity in agreement with the Coleman-Mandula theorem.

Structural studies of local environments in high-symmetry quasicrystals

The statistics of how the local environment of a particle looks like, e.g., given by the distribution of nearest neighbor distances or the sizes of Voronoi cells, is important as a starting point for the calculation of many material properties like electronic or photonic band structures. Here we study local environments that occur in quasicrystals with large rotational symmetry. Both with analytical considerations based on geometric arguments and with an analysis of a large number of numerically created patches of high-symmetry quasicrystals we find that the Voronoi area’s distribution reaches a bimodal curve and that in the limit of large rotational symmetries the distribution of nearest neighbor distance converges against a universal curve, where 27.7% of the vertices have their nearest neighbor at a normalized distance equal to 1, while for the other 72.3% the nearest neighbor is at a distance less than 1. Therefore, the statistics of local environments is non-trivial but independent of the specific rotational symmetry. Thus properties that only depend on local environments are expected to be universal for all high-symmetry quasicrystals.

Matrix Product Symmetries and Breakdown of Thermalization from Hard Rod Deformations.

We construct families of exotic spin-1/2 chains using a procedure called "hard rod deformation." We treat both integrable and nonintegrable examples. The models possess a large noncommutative symmetry algebra, which is generated by matrix product operators with a fixed small bond dimension. The symmetries lead to Hilbert space fragmentation and to the breakdown of thermalization. As an effect, the models support persistent oscillations in nonequilibrium situations. Similar symmetries have been reported earlier in integrable models, but here we show that they also occur in nonintegrable cases.

Itinerant ferromagnetism in SU(N)-symmetric fermi gases at finite temperature: first order phase transitions and time-reversal symmetry

At temperatures well below the Fermi temperature T F , the coupling of magnetic fluctuations to particle-hole excitations in a two-component Fermi gas leads to non-analytic corrections in the renormalized free energy and makes the transition to itinerant ferromagnetism first order. On the other hand, despite that larger symmetry often introduces larger degeneracies in the low-lying states, here we show that for a Fermi gas with SU(N > 2)-symmetry in three space dimensions the ferromagnetic phase transition is first order in agreement with the predictions of Landau’s mean-field theory in its minimal formulation, which contains a cubic term in the free-energy (Cazalilla et al 2009 New J. Phys. 11 103033). By performing unrestricted Hartree–Fock calculations for an SU(N > 2)-symmetric Fermi gas with short range interactions, we find the order parameter undergoes a finite jump across the transition. In addition, for SU(N > 2) we do not observe any tri-critical point up to temperatures , for which the thermal smearing of the Fermi surface and thermal fluctuations are substantial. Going beyond mean-field theory, we find that the coupling of magnetic fluctuations to particle-hole excitations makes the transition more abrupt and further enhances the tendency of the gas to become fully polarized for smaller values of N and the gas parameter . In our study, we also clarify the role of time reversal symmetry in the microscopic Hamiltonian and obtain the temperature dependence of Tan’s contact. For the latter, the presence of the tri-critical point for N = 2 leads to a more pronounced temperature dependence around the transition than for SU(N > 2)-symmetric gases. Although the results are obtained for a microscopic model relevant to ultracold atomic gases, they may also apply to models of solid state systems with SU(N > 2) symmetry provided Coulomb interactions are sufficiently well screened.

Invariant theory for the free left-regular band and a q-analogue

We examine from an invariant theory viewpoint the monoid algebras for two monoids having large symmetry groups. The first monoid is the free left-regular band on $n$ letters, defined on the set of all injective words, that is, the words with at most one occurrence of each letter. This monoid carries the action of the symmetric group. The second monoid is one of its $q$-analogues, considered by K. Brown, carrying an action of the finite general linear group. In both cases, we show that the invariant subalgebras are semisimple commutative algebras, and characterize them using Stirling and $q$-Stirling numbers. We then use results from the theory of random walks and random-to-top shuffling to decompose the entire monoid algebra into irreducibles, simultaneously as a module over the invariant ring and as a group representation. Our irreducible decompositions are described in terms of derangement symmetric functions introduced by D\'esarm\'enien and Wachs.

Isometry groups with radical, and aspherical Riemannian manifolds with large symmetry, I

Isometry groups with radical, and aspherical Riemannian manifolds with large symmetry, I

Recent Progress in Multiterminal Memristors for Neuromorphic Applications

AbstractThe essential step for developing neuromorphic systems is to construct more biorealistic elementary devices with rich spatiotemporal dynamics to exhibit highly separable responses in dynamic environmental circumstances. Unlike transistor‐based devices and circuits with zeroth‐order complexity, memristors intrinsically express some simple biomimetic functions. However, with only two‐terminal structure, precise control of operation principles to ensure large dynamic space, improved linearity and symmetry, multimodal operation as well as high‐order complexity is hard to achieve in a traditional memristor owing to its limited degree of freedom. Therefore, multiterminal memristors including both concrete terminals and virtual terminals (light, pressure, gas, ferroelectric polarity, etc.) have been proposed to obtain precise modulation of memristive characteristics. This review focuses on the recent progress in multiterminal memristors and their neuromorphic applications. The operation principle, application of multiterminal memristor on neuromorphic computing in different scenarios, existing challenges and future prospects are discussed.