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Results for “topological K matrix”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Continuous phase transition between bosonic integer quantum Hall liquid and a trivial insulator: Evidence for deconfined quantum criticality

The deconfined quantum critical point, a prototype Landau-forbidden transition, could exist, in principle, in the phase transitions involving a symmetry-protected topological phase; however, examples of such kinds of transitions in physical systems are rare beyond one-dimensional systems. Here, using a density-matrix renormalization-group calculation, we unveil a bosonic integer quantum Hall phase in a two-dimensional correlated honeycomb lattice, by full identification of its internal structure from the topological K matrix. Furthermore, we demonstrate that imbalanced periodic chemical potentials can destroy the bosonic integer quantum Hall state and drive it into a featureless trivial (Mott) insulator, where all physical observables evolve smoothly across the critical point. At the critical point, the entanglement entropy reveals a characteristic scaling behavior, which is consistent with the critical field theory as an emergent QED3 with two flavors of Dirac fermions.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Even spheres as joint spectra of matrix models

The Clifford spectrum is a form of joint spectrum for noncommuting matrices. This theory has been applied in photonics, condensed matter and string theory. In applications, the Clifford spectrum can be efficiently approximated using numerical methods, but this only is possible in low dimensional example. In this paper we examine the higher-dimensional spheres that can arise from theoretical examples. We also describe a constructive method to generate five real symmetric almost commuting matrices that have a K-theoretical obstruction to being close to commuting matrices. For this, we look to matrix models of topological electric circuits.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Unhinging the Surfaces of Higher-Order Topological Insulators and Superconductors

Here, we show that the chiral Dirac and Majorana hinge modes in three-dimensional higher-order topological insulators (HOTIs) and superconductors (HOTSCs) can be gapped while preserving the protecting C$_{2n}\mathcal{T}$ symmetry upon the introduction of non-Abelian surface topological order. In both cases, the topological order on a single side surface breaks time-reversal symmetry, but appears with its time-reversal conjugate on alternating sides in a C$_{2n}\mathcal{T}$ preserving pattern. In the absence of the HOTI/HOTSC bulk, such a pattern necessarily involves gapless chiral modes on hinges between C$_{2n}\mathcal{T}$-conjugate domains. However, using a combination of K -matrix and anyon condensation arguments, we show that on the boundary of a 3D HOTI/HOTSC these topological orders are fully gapped and hence “anomalous.” Our results suggest that new patterns of surface and hinge states can be engineered by selectively introducing topological order only on specific surfaces.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS2013

Development and Evaluation of an Order-N Formulation for Multi-Flexible Body Space Systems

This paper presents development of a generic recursive Order-N algorithm for systems with rigid and flexible bodies, in tree or closed-loop topology, with N being the number of bodies of the system. Simulation results are presented for several test cases to verify and evaluate the performance of the code compared to an existing efficient dense mass matrix-based code. The comparison brought out situations where Order-N or mass matrix-based algorithms could be useful.

Multibody dynamics↗
DOE OSTI2024

Extracting Higher Central Charge from a Single Wave Function

A (2+1)D topologically ordered phase may or may not have a gappable edge, even if its chiral central charge c_ is vanishing. Recently, it was discovered that a quantity regarded as a "higher" version of chiral central charge gives a further obstruction beyond c_ to gapping out the edge. Here, in this Letter, we show that the higher central charges can be characterized by the expectation value of the partial rotation operator acting on the wave function of the topologically ordered state. This allows us to extract the higher central charge from a single wave function, which can be evaluated on a quantum computer. Our characterization of the higher central charge is analytically derived from the modular properties of edge conformal field theory, as well as the numerical results with the ν = 1/2 bosonic Laughlin state and the non-Abelian gapped phase of the Kitaev honeycomb model, which corresponds to U(1) 2 and Ising topological order, respectively. The Letter establishes a numerical method to obtain a set of obstructions to the gappable edge of (2+1)D bosonic topological order beyond c_, which enables us to completely determine if a (2+1)D bosonic Abelian topological order has a gappable edge or not. We also point out that the expectation values of the partial rotation on a single wave function put a constraint on the low-energy spectrum of the bulk-boundary system of (2+1)D bosonic topological order, reminiscent of the Lieb-Schultz-Mattis-type theorems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Towards automating structural discovery in scanning transmission electron microscopy *

Abstract Scanning transmission electron microscopy is now the primary tool for exploring functional materials on the atomic level. Often, features of interest are highly localized in specific regions in the material, such as ferroelectric domain walls, extended defects, or second phase inclusions. Selecting regions to image for structural and chemical discovery via atomically resolved imaging has traditionally proceeded via human operators making semi-informed judgements on sampling locations and parameters. Recent efforts at automation for structural and physical discovery have pointed towards the use of ‘active learning’ methods that utilize Bayesian optimization with surrogate models to quickly find relevant regions of interest. Yet despite the potential importance of this direction, there is a general lack of certainty in selecting relevant control algorithms and how to balance a priori knowledge of the material system with knowledge derived during experimentation. Here we address this gap by developing the automated experiment workflows with several combinations to both illustrate the effects of these choices and demonstrate the tradeoffs associated with each in terms of accuracy, robustness, and susceptibility to hyperparameters for structural discovery. We discuss possible methods to build descriptors using the raw image data and deep learning based semantic segmentation, as well as the implementation of variational autoencoder based representation. Furthermore, each workflow is applied to a range of feature sizes including NiO pillars within a La:SrMnO 3 matrix, ferroelectric domains in BiFeO 3 , and topological defects in graphene. The code developed in this manuscript is open sourced and will be released at github.com/nccreang/AE_Workflows .

47 OTHER INSTRUMENTATION↗
DOE OSTI2025

Higher Hall conductivity from a single wave function: Obstructions to symmetry-preserving gapped edge of (2+1)-dimensional topological order

A (2+1)D topologically ordered phase with U(1) symmetry may or may not have a symmetric gapped edge state, even if both thermal and electric Hall conductivity are vanishing. It has recently been discovered that there are “higher” versions of Hall conductivity valid for fermionic fractional quantum Hall (FQH) states that obstruct symmetry-preserving gapped edge states beyond thermal and electric Hall conductivity. In this paper, we show that one can extract higher Hall conductivity from a single wave function of an FQH state, by evaluating the expectation value of the “partial rotation” unitary, which is a combination of partial spatial rotation and a U(1) phase rotation. This result is verified numerically with the fermionic Laughlin state with 𝜈=1/3 and 1/5, as well as the non-Abelian Moore-Read state. Together with topological entanglement entropy, we prove that the expectation values of the partial rotation completely determine if a bosonic/fermionic Abelian topological order with U(1) symmetry has a symmetry-preserving gappable edge state or not. We also show that thermal and electric Hall conductivity of Abelian topological order can be extracted by partial rotations. Even in non-Abelian FQH states, partial rotation provides the Lieb-Schultz-Mattis type theorem constraining the low-energy spectrum of the bulk-boundary system. The generalization of higher Hall conductivity to the case with Lie group symmetry is also presented.

2-dimensional systems↗
DOE OSTI2020

Role of matrix elements in the time-resolved photoemission signal

Time- and angle-resolved photoemission spectroscopy (TR-ARPES) provides access to the ultrafast evolution of electrons andmany-body interactions in solid-state systems. However, themomentum- and energy-resolved transient photoemission intensitymay not be unambiguously described by the intrinsic relaxation dynamics of photoexcited electrons alone.The interpretation of the time-dependent photoemission signal can be affected by the transient evolution of the electronic distribution, and both the one-electron removal spectral function aswell as the photoemissionmatrix elements. Here we investigate the topological insulator Bi 1.1 Sb 0.9 Te 2 S to demonstrate, bymeans of a detailed probe-polarization dependent study, the transient contribution ofmatrix elements toTR-ARPES.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Finite and infinite matrix product states for Gutzwiller projected mean-field wave functions

Matrix product states (MPS) and “dressed” ground states of quadratic mean fields (e.g., Gutzwiller projected Slater determinants) are both important classes of variational wave functions. This latter class has played important roles in understanding superconductivity and quantum spin liquids. We present a method to obtain both the finite and infinite MPS (iMPS) representation of the ground state of an arbitrary fermionic quadratic mean-field Hamiltonian (which in the simplest case is a Slater determinant and in the most general case is a Pfaffian). We also show how to represent products of such states (e.g., determinants times Pfaffians). From this representation one can project to single occupancy and evaluate the entanglement spectra after Gutzwiller projection. We then obtain the MPS and iMPS representation of Gutzwiller projected mean-field states that arise from the variational slave-fermion approach to the S = 1 bilinear-biquadratic quantum spin chain. To accomplish this, we develop an approach to orthogonalize degenerate iMPS to find all the states in the degenerate ground-state manifold. We find the energies of the MPS and iMPS states match the variational energies closely, indicating the method is accurate and there is minimal loss due to truncation error. We then present an exploration of the entanglement spectra of projected slave-fermion states, exploring their qualitative features and finding good qualitative agreement with the respective exact ground-state spectra found from density matrix renormalization group.

1-dimensional spin chains↗
DOE OSTI2021

Quantum Spin Torque Driven Transmutation of an Antiferromagnetic Mott Insulator

The basic model of spin-transfer torque (STT) in antiferromagnetic spintronics considers the exchange of angular momentum between quantum spins of flowing electrons and noncollinear-to-them localized spins treated as classical vectors. These vectors are assumed to realize Néel order in equilibrium, ↑ ↓ ∙∙∙ ↑ ↓, and their STT-driven dynamics is described by the Landau-Lifshitz-Gilbert (LLG) equation. However, many experimentally employed materials (such as archetypal NiO) are strongly electron-correlated antiferromagnetic Mott insulators (AFMIs) whose localized spins form a ground state quite different from the unentangled Néel state | ↑ ↓ ∙∙∙ ↑ ↓$\rangle$. The true ground state is entangled by quantum spin fluctuations, leading to the expectation value of all localized spins being zero, so that LLG dynamics of classical vectors of fixed length rotating due to STT cannot even be initiated. Instead, a fully quantum treatment of both conduction electrons and localized spins is necessary to capture the exchange of spin angular momentum between them, denoted as quantum STT. We use a recently developed time-dependent density matrix renormalization group approach to quantum STT to predict how injection of a spin-polarized current pulse into a normal metal layer coupled to an AFMI overlayer via exchange interaction and possibly small interlayer hopping—mimicking, e.g., topological-insulator/NiO bilayer employed experimentally—will induce a nonzero expectation value of AFMI localized spins. This new nonequilibrium phase is a spatially inhomogeneous ferromagnet with a zigzag profile of localized spins. The total spin absorbed by AFMI increases with electron-electron repulsion in AFMIs, as well as when the two layers do not exchange any charge.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1989

A class of parallel algorithms for computation of the manipulator inertia matrix

Parallel and parallel/pipeline algorithms for computation of the manipulator inertia matrix are presented. An algorithm based on composite rigid-body spatial inertia method, which provides better features for parallelization, is used for the computation of the inertia matrix. Two parallel algorithms are developed which achieve the time lower bound in computation. Also described is the mapping of these algorithms with topological variation on a two-dimensional processor array, with nearest-neighbor connection, and with cardinality variation on a linear processor array. An efficient parallel/pipeline algorithm for the linear array was also developed, but at significantly higher efficiency.

Fijany, Amir↗
DOE OSTI2020

The changing mouse embryo transcriptome at whole tissue and single-cell resolution

During mammalian embryogenesis, differential gene expression gradually builds the identity and complexity of each tissue and organ system 1 . Here we systematically quantified mouse polyA-RNA from day 10.5 of embryonic development to birth, sampling 17 tissues and organs. The resulting developmental transcriptome is globally structured by dynamic cytodifferentiation, body-axis and cell-proliferation gene sets that were further characterized by the transcription factor motif codes of their promoters. We decomposed the tissue-level transcriptome using single-cell RNA-seq (sequencing of RNA reverse transcribed into cDNA) and found that neurogenesis and haematopoiesis dominate at both the gene and cellular levels, jointly accounting for one-third of differential gene expression and more than 40% of identified cell types. By integrating promoter sequence motifs with companion ENCODE epigenomic profiles, we identified a prominent promoter de-repression mechanism in neuronal expression clusters that was attributable to known and novel repressors. Focusing on the developing limb, single-cell RNA data identified 25 candidate cell types that included progenitor and differentiating states with computationally inferred lineage relationships. We extracted cell-type transcription factor networks and complementary sets of candidate enhancer elements by using single-cell RNA-seq to decompose integrative cis -element (IDEAS) models that were derived from whole-tissue epigenome chromatin data. These ENCODE reference data, computed network components and IDEAS chromatin segmentations are companion resources to the matching epigenomic developmental matrix, and are available for researchers to further mine and integrate.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Anomalous Hall effect in conical helimagnetic crystals

Spin-spiral texture can substantially change charge transport properties in helimagnets. Here we find the anomalous Hall effect (AHE) exhibiting the dramatic behavior with respect to chemical potential μ in conical magnetic structures. The direct conductivity demonstrates kinks, and the anomalous Hall current exhibits minima and maxima changing the sign. We analytically derive the expression for energy bands and eigenstates in the most general case. Because of the conical potential, the energy bands are split into two nonparabolic bands where the lower band can have one- or two-minima shapes in the k z direction ($\hat{z}$ is a direction of the spiral axis). We prove that the origin of the anomalous Hall effect is not topological and is due to the interplay between the asymmetry of energy bands in the x and z directions and spin restrictions in the phase space due to the conical potential. We also investigate the dependence of transport properties on cone half- angle θ, and find that the effects are most pronounced at θ=π/2 (a helical state). Electric current is calculated using the Boltzmann equation where the relaxation is caused by electron-acoustic phonon interaction. The transition probability is found to be a 2×2 matrix with nonvanishing off-diagonal elements indicating the strong interband transitions. The origin of interband transitions is because of the nature of the conical potential where conduction electron spins interact with localized magnetic moments. To verify the proposed theory, we calculate the temperature dependence of resistivity for MnSi crystals and find the discontinuity at the phase transition between conical and paramagnetic phases. The calculations are in the excellent agreement with the experimental data. In addition, we predict the discontinuity behavior for the anomalous Hall resistivity at the phase transition where the resistivity exhibits the abrupt change at T=T C , (a) to zero if the relativistic effects for the conduction electrons are small or (b) to a nonzero value if Rashba/Dresselhaus effects are taken into account.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Amplifying Nanoparticle Reinforcement through Low Volume Topologically Controlled Chemical Coupling

Here, we present a streamlined method to covalently bond hydroxylated carbon nanotubes (CNOH) within a polyphenol matrix, all achieved through a direct, solvent-free process. Employing an extremely small concentration of CNOH (0.01% w/w) along with topologically contrasting linkers led to a maximum of 5-fold increase in modulus and a 25% enhancement in tensile strength compared to the unaltered matrix, an order of magnitude greater reinforcement (w/w) compared to state-of-the-art melt-processed nanocomposites. Through dynamic mechanical analysis, low field solid-state nuclear magnetic resonance spectroscopy, and molecular dynamics simulations, we uncovered the profound influence of linker’s conformational degrees of freedom on the segmental dynamics and therefore the material’s properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

An effective matrix model for dynamical end of the world branes in Jackiw-Teitelboim gravity

We study Jackiw-Teitelboim gravity with dynamical end of the world branes in asymptotically nearly AdS2 spacetimes. We quantize this theory in Lorentz signature, and compute the Euclidean path integral summing over topologies including dynamical branes. The latter will be seen to exactly match with a modification of the SSS matrix model. The resolution of UV divergences in the gravitational instantons involving the branes will lead us to understand the matrix model interpretation of the Wilsonian effective theory perspective on the gravitational theory. We complete this modified SSS matrix model nonperturbatively by extending the integration contour of eigenvalues into the complex plane. Furthermore, we give a new interpretation of other phases in such matrix models. We derive an effective W(Φ) dilaton gravity, which exhibits similar physics semiclassically. In the limit of a large number of flavors of branes, the effective extremal entropy S0,eff has the form of counting the states of these branes.

2D Gravity↗
DOE OSTI2026

A Fast Algorithm for Computing Zigzag Representatives

Zigzag filtrations of simplicial complexes generalize the usual filtrations by allowing simplex deletions in addition to simplex insertions. The barcodes computed from zigzag filtrations encode the evolution of homological features. Although one can locate a particular feature at any index in the filtration using existing algorithms, the resulting representatives may not be compatible with the zigzag: a representative cycle at one index may not map into a representative cycle at its neighbor. For this, one needs to compute compatible representative cycles along each bar in the barcode. It is known that the barcode for a zigzag filtration with m insertions and deletions can be computed $O(m^ω)$ in time, where $ω < 2.373$ is the matrix multiplication exponent. However, it is not known how to compute the compatible representatives so efficiently. For a non-zigzag filtration, the classical matrix-based algorithm provides representatives in $O(m^3)$ time, which can be improved to $O(m^ω)$. However, no known algorithm for zigzag filtrations computes the representatives with the $O(m^3)$ time bound. We present an $O(m^3 n)$ time algorithm for this problem, where $n ≤ m$ is the size of the largest complex in the filtration.

Persistent homology↗
DOE OSTI2024

Reducing crystal symmetry to generate out-of-plane Dzyaloshinskii–Moriya interaction

The Dzyaloshinskii-Moriya antisymmetric exchange interaction (DMI) stabilises topological spin textures with promising future spintronics applications. According to crystal symmetry, the DMI can be categorized as four different types that favour different chiral textures. Unlike the other three extensively-investigated types, out-of-plane DMI, as the last type that favours in-plane chirality, remained missing so far. Here we apply point-group-dependent DMI matrix analysis to show that out-of-plane DMI exists under reduced crystal symmetry. Through strain and structure engineering, we show how C s symmetry is realized in ultrathin magnets and observe the out-of-plane DMI stabilised in-plane chirality using spin-polarized electron microscopy. Our results show that extremely low out-of-plane DMI strengths at µeV/atom are sufficient to stabilise topological spin textures, including merons and bimerons. We also demonstrate field-induced reversible control of the in-plane chirality and merons. Our findings open up untapped paths on topological magnetic textures and their potential applications.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Topological terms with qubit regularization and relativistic quantum circuits

Qubit regularization provides a rich framework to explore quantum field theories. The freedom to choose how the important symmetries of the theory are embedded in the qubit regularization scheme allows us to construct new lattice models with rich phase diagrams. Some of the phases can contain topological terms which lead to critical phases. In this work we introduce and study the SU(3)-F qubit regularization scheme to embed the SO(3) spin-symmetry. We argue that qubit models in this regularization scheme contain several phases including a critical phase which describes the k = 1 Wess-Zumino-Witten (WZW) conformal field theory (CFT) at long distances, and two massive phases one of which is trvially gapped and the other which breaks the lattice translation symmetry. We construct a simple space-time Euclidean lattice model with a single coupling U and study it using the Monte Carlo method. We show the model has a critical phase at small U and a trivially massive phase at large U with a first order transition separating the two. Another feature of our model is that it is symmetric under space-time rotations, which means the temporal and spatial lattice spacing are connected to each other. The unitary time evolution operator obtained by a Wick rotation of the transfer matrix of our model can help us compute the physics of the k = 1 WZW CFT in real time without the need for tuning the temporal lattice spacing to zero. We use this idea to introduce the concept of a relativistic quantum circuit on a discrete space-time lattice.

Bhattacharya, Tanmoy↗