Search NASA⌕ Search

SEARCH · Search NASA

Results for “Topological Quantum Numbers”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2

The sponge-like topology of large-scale structure in the universe

The relative connectedness of the high- and low-density regions in the universe is studied using a median density contour which divides space into two equal volumes. The CfA data are found to show a sponge-like topology where the highand low-density regions are both interlocking and equivalent. The boundary surface between the two regions has a general negative curvature, and is characterized by a large number of holes. In the initial conditions the connectedness of the two regions must be identical because a change of sign in the random quantum fluctuations would reverse their roles. It is noted that in the cold dark matter and neutrino scenarios the hole sizes are typically of the order of the smoothing diameter or the damping length, whichever is larger. The sponge-like topology is consistent with the universe having a frothy appearance without being divided neatly into cells. A computer algorithm for measuring topology is discussed.

Gott, J. R., III↗

Probing Quantum Anomalous Hall States in Twisted Bilayer WSe 2 via Attractive Polaron Spectroscopy

Moiré superlattices in semiconductors exhibit a rich variety of interaction-induced topological states, including quantum anomalous Hall (QAH) effects. A recent study hinted that twisted WSe 2 homobilayer (tWSe 2 ) could host a QAH state but lacked direct evidence of ferromagnetism, a key hallmark of this phase. Here, we report the first direct evidence of QAH states in tWSe 2 with spontaneous ferromagnetism. Specifically, we employ polarization-resolved attractive polaron spectroscopy on a dual-gated, 2° tWSe 2 and observe direct signatures of spontaneous time-reversal symmetry breaking at hole filling 𝜈 = 1. Together with a Chern number (𝐶) measurement via Streda formula analysis, we identify this magnetized state as a topological state, characterized by 𝐶 = 1. Furthermore, we demonstrate that these topological and magnetic properties are tunable via a finite displacement field, between a QAH ferromagnetic state and an antiferromagnetic state. Our findings position tWSe 2 as a highly versatile, stable, and optically addressable platform for investigating topological order and strong correlations in two-dimensional landscapes.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Theory of topological exciton insulators and condensates in flat Chern bands

Excitons are the neutral quasiparticles that form when Coulomb interactions create bound states between electrons and holes. Due to their bosonic nature, excitons are expected to condense and exhibit superfluidity at sufficiently low temperatures. In interacting Chern insulators, excitons may inherit the nontrivial topology and quantum geometry from the underlying electron wavefunctions. We theoretically investigate the excitonic bound states and superfluidity in flat-band insulators pumped with light. We find that the exciton wavefunctions exhibit vortex structures in momentum space, with the total vorticity being equal to the difference of Chern numbers between the conduction and valence bands. Moreover, both the exciton binding energy and the exciton superfluid density are proportional to the Brillouin-zone average of the quantum metric and the Coulomb potential energy per unit cell. Spontaneous emission of circularly polarized light from radiative decay is a detectable signature of the exciton vorticity. We propose that the vorticity can also be experimentally measured via the nonlinear anomalous Hall effect, whereas the exciton superfluidity can be detected by voltage-drop quantization through a combination of quantum geometry and Aharonov–Casher effect. Topological excitons and their superfluid phase could be realized in flat bands of twisted Van der Waals heterostructures.

Science & Technology - Other Topics↗

Efficient Hamiltonian encoding algorithms for extracting quantum control mechanism as interfering pathway amplitudes in the Dyson series

Hamiltonian encoding is a methodology for revealing the mechanism behind the dynamics governing controlled quantum systems. In this paper, following Mitra and Rabitz \cite{abhra_1}, we define mechanism via pathways of eigenstates that describe the evolution of the system, where each pathway is associated with a complex-valued amplitude corresponding to a term in the Dyson series. The evolution of the system is determined by the constructive and destructive interference of these pathway amplitudes. Pathways with similar attributes can be grouped together into pathway classes. The amplitudes of pathway classes are computed by modulating the Hamiltonian matrix elements and decoding the subsequent evolution of the system rather than by direct computation of the individual terms in the Dyson series. The original implementation of Hamiltonian encoding was computationally intensive and became prohibitively expensive in large quantum systems. This paper presents two new encoding algorithms that calculate the amplitudes of pathway classes by using techniques from graph theory and algebraic topology to exploit patterns in the set of allowed transitions, greatly reducing the number of matrix elements that need to be modulated. These new algorithms provide an exponential decrease in both computation time and memory utilization with respect to the Hilbert space dimension of the system. To demonstrate the use of these techniques, they are applied to two illustrative state-to-state transition problems.

Abrams, Erez [Princeton University, Massachusetts ↗

Probing the Kitaev honeycomb model on a neutral-atom quantum computer

Quantum simulations of many-body systems are among the most promising applications of quantum computers. In particular, models based on strongly correlated fermions are central to our understanding of quantum chemistry and materials problems, and can lead to exotic, topological phases of matter. However, owing to the non-local nature of fermions, such models are challenging to simulate with qubit devices. Here we realize a digital quantum simulation architecture for two-dimensional fermionic systems based on reconfigurable atom arrays. We utilize a fermion-to-qubit mapping based on Kitaev’s model on a honeycomb lattice, in which fermionic statistics are encoded using long-range entangled states. We prepare these states efficiently using measurement and feedforward, realize subsequent fermionic evolution through Floquet engineering with tunable entangling gates interspersed with atom rearrangement, and improve results with built-in error detection. Leveraging this fermion description of the Kitaev spin model, we efficiently prepare topological states across its complex phase diagram and verify the non-Abelian spin-liquid phase by evaluating an odd Chern number. We further explore this two-dimensional fermion system by realizing tunable dynamics and directly probing fermion exchange statistics. Finally, we simulate strong interactions and study the dynamics of the Fermi–Hubbard model on a square lattice. These results pave the way for digital quantum simulations of complex fermionic systems for materials science, chemistry and high-energy physics.

atomic and molecular physics↗

Ordering the topological order in the fractional quantum Hall effect

Here, we discuss the possible topological order/topological quantum field theory of different quantum Hall systems. Given the value of the Hall conductivity, we constrain the global symmetry of the low-energy theory and its anomaly. Specifically, the one-form global symmetry and its anomaly are presented as the organizing principle of these systems. This information is powerful enough to lead to a unique minimal topological order (or a small number of minimal topological orders). Almost all of the known experimentally discovered topological orders are these minimal theories. Since this work is interdisciplinary, we made a special effort to relate to researchers with different backgrounds by providing translations between different perspectives.

Anyons↗

Solving the Bernstein-Vazirani problem using Majorana-based topological quantum algorithms

Executing quantum algorithms using Majorana zero modes—a major milestone for the field of topological quantum computing—requires a platform that can be scaled to large quantum registers, can be controlled in real time and space, and a braiding protocol that uses the unique properties of these exotic particles. Here, we demonstrate the first successful simulation of a Majorana-based, fault-tolerant quantum algorithm to solve the Bernstein-Vazirani problem in two-dimensional magnet-superconductor hybrid structures from initialization to read-out of the final many-body state. Utilizing the Majorana zero modes’ topological properties, we introduce an optimized braiding protocol for the algorithm and a scalable architecture for its implementation with an arbitrary number of qubits. We visualize the algorithm protocol in real time and space by computing the non-equilibrium density of states, which is proportional to the time-dependent differential conductance, and the non-equilibrium charge density, which assigns a unique signature to each final state of the algorithm.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Topological heavy fermions in magnetic field

The recently introduced topological heavy fermion model (THFM) provides a means for interpreting the low-energy electronic degrees of freedom of the magic angle twisted bilayer graphene as hybridization amidst highly dispersing topological conduction and weakly dispersing localized heavy fermions. In order to understand the Landau quantization of the ensuing electronic spectrum, a generalization of THFM to include the magnetic field B is desired, but currently missing. Here we provide a systematic derivation of the THFM in B and solve the resulting model to obtain the interacting Hofstadter spectra for single particle charged excitations. While naive minimal substitution within THFM fails to correctly account for the total number of magnetic subbands within the narrow band i.e., its total Chern number, our method—based on projecting the light and heavy fermions onto the irreducible representations of the magnetic translation group— reproduces the correct total Chern number. Analytical results presented here offer an intuitive understanding of the nature of the (strongly interacting) Hofstadter bands.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quantum Nonlinear Acoustic Hall Effect and Inverse Acoustic Faraday Effect in Dirac Insulators

Here, we propose to realize the quantum nonlinear Hall effect and the inverse Faraday effect through the acoustic wave in a time-reversal invariant but inversion broken Dirac insulator. We focus on the acoustic frequency much lower than the Dirac gap such that the interband transition is suppressed and these effects arise solely from the intrinsic valley-contrasting band topology. The corresponding acoustoelectric conductivity and magnetoacoustic susceptibility are both proportional to the quantized valley Chern number and independent of the quasiparticle lifetime. The linear and nonlinear components of the longitudinal and transverse topological currents can be tuned by adjusting the polarization and propagation directions of the surface acoustic wave. The static magnetization generated by a circularly polarized acoustic wave scales linearly with the acoustic frequency as well as the strain-induced charge density. Our results unveil a quantized nonlinear topological acoustoelectric response of gapped Dirac materials, like hexagonal boron nitride and transition-metal dichalcogenide, paving the way toward room-temperature acoustoelectric devices due to their large band gaps.

36 MATERIALS SCIENCE↗

Cornering relative symmetry theories

The symmetry data of a 𝑑-dimensional quantum field theory (QFT) can often be captured in terms of a higher-dimensional symmetry topological field theory. In top-down (i.e., stringy) realizations of this structure, the QFT in question is localized in a higher-dimensional bulk. In many cases of interest, however, the associated (𝑑+1)-dimensional bulk is not fully gapped and one must instead consider a filtration of theories to reach a gapped bulk in 𝐷 =𝑑 + 𝑚 dimensions. Overall, this leads us to a nested structure of relative symmetry theories which descend to coupled edge modes, with the original QFT degrees of freedom localized at a corner of this 𝐷-dimensional bulk system. We present a bottom-up characterization of this structure and also show how it naturally arises in a number of string-based constructions of QFTs with both finite and continuous symmetries.

M-theory↗

Switching and Rectification in Carbon-Nanotube Junctions

Multi-terminal carbon-nanotube junctions are under investigation as candidate components of nanoscale electronic devices and circuits. Three-terminal "Y" junctions of carbon nanotubes (see Figure 1) have proven to be especially interesting because (1) it is now possible to synthesize them in high yield in a controlled manner and (2) results of preliminary experimental and theoretical studies suggest that such junctions could exhibit switching and rectification properties. Following the preliminary studies, current-versus-voltage characteristics of a number of different "Y" junctions of single-wall carbon nanotubes connected to metal wires were computed. Both semiconducting and metallic nanotubes of various chiralities were considered. Most of the junctions considered were symmetric. These computations involved modeling of the quantum electrical conductivity of the carbon nanotubes and junctions, taking account of such complicating factors as the topological defects (pentagons, heptagons, and octagons) present in the hexagonal molecular structures at the junctions, and the effects of the nanotube/wire interfaces. A major component of the computational approach was the use of an efficient Green s function embedding scheme. The results of these computations showed that symmetric junctions could be expected to support both rectification and switching. The results also showed that rectification and switching properties of a junction could be expected to depend strongly on its symmetry and, to a lesser degree, on the chirality of the nanotubes. In particular, it was found that a zigzag nanotube branching at a symmetric "Y" junction could exhibit either perfect rectification or partial rectification (asymmetric current-versus-voltage characteristic, as in the example of Figure 2). It was also found that an asymmetric "Y" junction would not exhibit rectification.

Srivastava, Deepak↗

Degenerate domain walls in supersymmetric theories

In supersymmetric Yang–Mills theories tension-degenerate domain walls are typical. Adding matter fields in fundamental representation, we arrive at supersymmetric quantum chromodynamics (SQCD) supporting similar walls. We demonstrate that the degenerate domain walls can belong to one of two classes: i) locally distinguishable, i.e. those which differ from each other locally (which could be detected in local measurements); and ii) those which have identical local structure and are differentiated only topologically, through a judicially chosen compactification of R 4 . Depending on the number of flavors F and the pattern of Higgsing, both classes can coexist among SQCD k walls interpolating between the vacua n and n + k . We prove that the overall multiplicity of the domain walls obtained after accounting for both classes is ν N , k walls = N ! / [ ( N − k ) ! k ! ] , as was discovered previously in limiting cases. (Here, N is the number of colors.) Thus, ν N , k walls is a peculiar index. For the locally distinguishable degenerate domain walls, we observe two-wall junctions, a phenomenon specific for supersymmetry with central extensions. This phenomenon does not exist for topological replicas.

Chen, Shi↗

Para-particle oscillator simulations on a trapped-ion quantum computer

Deformed oscillators allow for a generalization of the standard fermions and bosons, namely, for the description of para-particles. Such particles remain hypothetical and unobserved in nature; yet, they can model physical phenomena, such as topological phases of matter. Here, we report the digital quantum simulation of para-particle oscillators by mapping para-particle states to the state of a qubit register, which allows us to identify the para-particle oscillator Hamiltonian as an XY model and further digitize the system onto a universal set of gates. In both instances, the gate depth grows polynomially with the number of qubits used. To establish the validity of our results, we experimentally simulate the dynamics of para-fermions and para-bosons, demonstrating full control of para-particle oscillators on a quantum computer. Furthermore, we compare the overall performance of the digital simulation of dynamics of the driven para-Fermi oscillator to a recent analog quantum simulation result.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

EuAuSb: An odd-parity helical variation of altermagnetism

EuAuSb is a triangular-lattice Dirac semimetal in which a topological Hall effect has been observed to develop in association with a magnetically ordered phase. Our single-crystal neutron diffraction measurements have identified an incommensurate helical order in which individual ferromagnetic Eu 2+ layers rotate in-plane by ∼ 120° from one layer to the next. An in-plane magnetic field distorts the incommensurate order, eventually leading to a first order transition to a state that is approximately commensurate and that is continuously polarized as the bulk magnetization approaches saturation. From an analysis of the magnetic diffraction intensities versus field, we find evidence for a dip in the ordered in-plane moment at the same field where the topological Hall effect is a maximum, and we propose that this is due to field-induced quantum spin fluctuations. Our electronic structure calculations yield exchange constants compatible with the helical order and show that the bands near the Fermi level lose their spin degeneracy via a mechanism similar to that in the collinear altermagnets. In conclusion, we find that, unlike the even symmetry seen in the altermagnets, the spin splitting in EuAuSb has odd-wave symmetry similar to that recently found in a number of coplanar magnetic materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Generalized Hall conductivities in local commuting projector models: Generalized symmetries and protected surface modes

Hall conductivities are important characterizations of phases of matter. It is known that nonzero Hall conductivities are difficult to realize in local commuting projector lattice models due to no-go theorems in (2+1)⁢D. In this work we construct local commuting projector models in (2+1)⁢D and (3+1)⁢D with nonzero generalized Hall conductivities for ordinary and higher-form continuous symmetries on tensor product Hilbert space of finite local dimension. The model is given by a standard ℤ 𝑁 toric code, but the symmetries do not admit expression in terms of on-site charge operators. The symmetry do not have local charges or currents on the lattice in the absence of boundaries, but there is still a notion of Hall conductivities that coincide with the continuum field theories. We construct protected gapless boundaries of the lattice models using modified Villain formalism. The generalized Hall conductivities are computed by surface currents as well as bulk flux insertion and many-body Chern number.

Anomalies↗

Quantum/AI Topology-Aware Latency-Adaptive HPC Workflow Scheduling Optimization

The growing demand for more powerful high-performance computing (HPC) systems has led to a steady rise in energy consumption by supercomputing worldwide. This study is focused on comparing our Application-Topology Mapper (ATMapper) to the popular Simple Linux Utility for Resource Management (SLURM) for the purpose of exploring methods that can further optimize job-scheduling within HPC systems. ATMapper is an Artificial-Intelligence based approach to job-scheduling that is currently being enhanced with quantum annealing (QA) to generate optimal schedules faster. We are applying QA to speedup our ATMapper process to achieve higher computing efficiency, thereby reducing HPC energy consumption. Here, we examine how four job-scheduling approaches perform in processor node assignment when using an example network architecture of 4 interconnected nodes. Using a specialized script, we are assessing the schedule of a computation flow with 11 interdependent tasks. The data movements among nodes were tracked to count for the number of interactions (network hops) between nodes needed to complete the tasks. The total number of hops and the job completion time were then used to quantify the efficiency of the different mapping approaches. In addition to SLURM, we also compare our ATMapper to the QA-enabled LBNL TIGER and the D-Wave Distributed Computing processor assignment approaches. The preliminary results showed that our topology-aware, latency-adaptive ATMapper is significantly more efficient when compared to the other scheduling approaches due to its load-imbalance network allocation. The scheduler displayed a computing efficiency of 53% by performing significantly fewer network hops than its alternatives. By reducing the number of hops, ATMapper was able to perform all 11 tasks by using only 3 nodes out of given 4. This research indicates the potential to use QA/AI for HPC job-scheduling. Later, we will test a SLURM simulator program to draw further comparisons on the effectiveness of ATMapper's scheduling approach. The results of this comparison will serve as a baseline for later improving SLURM's performance using a QA-enhanced ATMapper approach.

Caraveo, Braulio [University of Huston - Clear Lak↗

Understanding baryon stopping at the BNL Relativistic Heavy Ion Collider top energies

The nucleon exhibits a rich internal structure governed by quantum chromodynamics (QCD), where its electric charge arises from valence quarks, while its spin and mass emerge from complex interactions among valence quarks, sea (anti)quarks, and gluons. At the advent of QCD, an alternative hypothesis emerged suggesting, at high energies, the transport of a nucleon's baryon number could be traced by a nonperturbative configuration of gluon fields connecting its three valence quarks, forming a 𝑌-shaped topology known as the gluon junction. Recent measurements by the STAR experiment are compatible with this scenario. In light of these measurements, this study aims to explore the mechanisms of baryon transport in high-energy nuclear collisions using the pythia-8 framework, which incorporates a state-of-the-art hadronization model with advanced color flow (CF) and color reconnection (CR) mechanisms that mimic signatures of a baryon junction. Within this model setup, we investigate (i) the rapidity slope of the net-baryon distributions in photon-included processes (𝛾 + 𝑝) and (ii) baryon over charge transport in the isobaric (Ru + Ru and Zr + Zr) collisions. Our study highlights the importance of the CF and CR mechanisms in pythia-8, which play a crucial role in baryon transport. The results show that the CF and CR schemes significantly affect the isobaric baryon-to-charge ratio, leading to different predictions for baryon stopping and underscoring the need to account for CF and CR effects in comparisons with experimental measurements.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes

Studies of many-body non-Hermitian parity-time (PT)-symmetric quantum systems are attracting a lot of interest due to their relevance in research areas ranging from quantum optics and continuously monitored dynamics to Euclidean wormholes in quantum gravity and dissipative quantum chaos. While a symmetry classification of non-Hermitian systems leads to 38 universality classes, we show that, under certain conditions, PT-symmetric systems are grouped into 24 universality classes. We identify 14 of them in a coupled two-site Sachdev-Ye-Kitaev (SYK) model and confirm the classification by spectral analysis using exact diagonalization techniques. Intriguingly, in 4 of these 14 universality classes, AIII ν , BDI ν † , BDI + + ν , and CI − − ν , we identify a basis in which the SYK Hamiltonian has a block structure in which some blocks are rectangular, with ν ∈ N the difference between the number of rows and columns. We show analytically that this feature leads to the existence of ν robust purely eigenvalues, whose level statistics follow the predictions of Hermitian random matrix theory for classes A, AI, BDI, and CI, respectively. We have recently found that this ν is a topological invariant, so these classes are topological. By contrast, nontopological real eigenvalues display a crossover between Hermitian and non-Hermitian level statistics. Similarly to the case of Lindbladian dynamics, the reduction of universality classes leads to unexpected results, such as the absence of Kramers degeneracy in a given sector of the theory. Another novel feature of the classification scheme is that different sectors of the PT-symmetric Hamiltonian may have different symmetries. Published by the American Physical Society 2024

Astronomy & Astrophysics↗