Boundary Hamiltonian Theory for Gapped Topological Orders

We report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces, with explicit boundary terms. We do this mainly for the Levin-Wen string-net model. The full Hamiltonian in our approach yields a topologically protected, gapped energy spectrum, with the corresponding wave functions robust under topology-preserving transformations of the lattice of the system. We explicitly present the wavefunctions of the ground states and boundary elementary excitations. The creation and hopping operators of boundary quasi-particles are constructed. It is found that given a bulk topological order, the gapped boundary conditions are classified by Frobenius algebras in its input data. Emergent topological properties of the ground states and boundary excitations are characterized by （bi-） modules over Frobenius algebras.

Discovery of Fractionalized Neutral Spin-1/2 Excitation of Topological Order

After the discovery of fraction quantum Hall states in the 1980s, it became more and more clear that Landau symmetry breaking theory does not describe all possible quantum phases of matter. The new quan- tum phases of matter were called topologically ordered phases（for gapped cases） or quantum ordered phases （for gapless cases）, which correspond to pat- terns of many-body entanglement. One may won- der： besides quantum Hall systems, are there other systems that realize the new topological/quantum order？

Separation axioms in topological ordered spaces

The Ti-axiom,the Ti-ordered axiom and Ti-pairwise axiom(i = 0,1,2,3,4) of topological ordered space are discussed and proved that they are equivalence under the certain conditions.

Counting and Topological Order

The counting method is a simple and efficient method for processing linear recursive datalog queries. Its time complexity is bounded by O(n.e), where n and e denote the numbers of nodes and edges, respectively, in the graph representing the input relations. In this paper, the concepts of heritage appearance function and heritage selection function are introduced, and an evaluation algorithm based on the computation of such functions in topological order is developed. This new algorithm requires only linear time in the case of non-cyclic data.

Experimental probing topological order and its breakdown through modular matrices

With the support by the National Natural Science Foundation of China,a collaborative study by the research groups led by Prof.Du Jiangfeng(杜江峰)and Prof.Peng Xinhua(彭新华)from the CAS Key Laboratory of Microscale Magnetic Resonance,University of Science and Technology of China,and Prof.

γ and β Approximations via General Ordered Topological Spaces

In this paper, we introduce the concepts of g and b approximations via general ordered topological approximation spaces. Also, increasing (decreasing) g, b boundary, positive and negative regions are given in general ordered topological approximation spaces (GOTAS, for short). Some important properties of them were investigated. From this study, we can say that studying any properties of rough set concepts via GOTAS is a generalization of Pawlak approximation spaces and general approximation spaces.

A Multi-Object Genetic Algorithm for the Assembly Line Balance Optimization in Garment Flexible Job Shop Scheduling

Numerous clothing enterprises in the market have a relatively low efficiency of assembly line planning due to insufficient optimization of bottleneck stations.As a result,the production efficiency of the enterprise is not high,and the production organization is not up to expectations.Aiming at the problem of flexible process route planning in garment workshops,a multi-object genetic algorithm is proposed to solve the assembly line bal-ance optimization problem and minimize the machine adjustment path.The encoding method adopts the object-oriented path representation method,and the initial population is generated by random topology sorting based on an in-degree selection mechanism.The multi-object genetic algorithm improves the mutation and crossover operations according to the characteristics of the clothing process to avoid the generation of invalid offspring.In the iterative process,the bottleneck station is optimized by reasonable process splitting,and process allocation conforms to the strict limit of the station on the number of machines in order to improve the compilation efficiency.The effectiveness and feasibility of the multi-object genetic algorithm are proven by the analysis of clothing cases.Compared with the artificial allocation process,the compilation efficiency of MOGA is increased by more than 15%and completes the optimization of the minimum machine adjustment path.The results are in line with the expected optimization effect.

Larger in-plane upper critical field and superconducting diode effect observed in topological superconductor candidate InNbS_(2)nanoribbons

Recently,the coexistence of topology and superconductivity has garnered considerable attention.Specifically,the dimensionality of these materials is crucial for the realization of topological quantum computation.However,the naturally grown materials,especially with one-dimensional feature that exhibits the coexistence of topology and superconductivity,still face challenges in terms of experimental realization and scalability,which hinders the fundamental research development and the potential to revolutionize quantum computing.Here,we report the first experimental synthesis of quasi-one-dimensional InNbS_(2)nanoribbons that exhibit the coexistence of topological order and superconductivity via a chemical vapor transport method.Especially,the inplane upper critical field of InNbS_(2)nanoribbons exceeds the Pauli paramagnetic limit by more than 2.2 times,which can be attributed to the enhanced spin-orbit coupling and the weakened interlayer interaction between the NbS_(2)layers induced by the insertion of In atoms,making InNbS_(2)exhibit spin-momentum locking similar to that of monolayer NbS_(2).Moreover,for the first time,we report the superconducting diode effect in a quasi-one-dimensional superconductor system without any inherent geometric imperfections.The measured maximum efficiency is manifested as 14%,observed atμ0H≈±60 mT,and we propose that the superconducting diode effect can potentially be attributed to the presence of the nontrivial topological band.Our work provides a platform for studying exotic phenomena in condensed matter physics and potential applications in quantum computing and quantum information processing.

Combining Self-Organizing Map and Lipschitz Condition for Estimation in Direction of Arrival

There are many DOA estimation methods based on different signal features, and these methods are often evaluated by experimental results, but lack the necessary theoretical basis. Therefore, a direction of arrival (DOA) estimation system based on self-organizing map (SOM) and designed for arbitrarily distributed sensor array is proposed. The essential principle of this method is that the map from distance difference of arrival (DDOA) to DOA is Lipschitz continuity, it indicates the similar topology between them, and thus Kohonen SOM is a suitable network to classify DOA through DDOA. The simulation results show that the DOA estimation errors are less than 1° for most signals between 0° to 180°. Compared to MUSIC, Root-MUSIC, ESPRIT, and RBF, the errors of signals under signal-to-noise ratios (SNR) declines from 20 dB to 2 dB are robust, SOM is better than RBF and almost close to MUSIC. Further, the network can be trained in advance, which makes it possible to be implemented in real-time.

Entanglement spectrum of non-Abelian anyons

Non-Abelian anyons can emerge as fractionalized excitations in two-dimensional systems with topological order. One important example is the Moore–Read fractional quantum Hall state. Its quasihole states are zero-energy eigenstates of a parent Hamiltonian, but its quasiparticle states are not. Both of them can be modeled on an equal footing using the bipartite composite fermion method. We study the entanglement spectrum of the cases with two or four non-Abelian anyons. The counting of levels in the entanglement spectrum can be understood using the edge theory of the Moore–Read state, which reflects the topological order of the system. It is shown that the fusion results of two non-Abelian anyons is determined by their distributions in the bipartite construction.

Ground-state information geometry and quantum criticality in an inhomogeneous spin model

We investigate the ground-state Riemannian metric and the cyclic quantum distance of an inhomogeneous quantum spin-1/2 chain in a transverse field. This model can be diagonalized by using a general canonical transformation to the fermionic Hamiltonian mapped from the spin system. The ground-state Riemannian metric is derived exactly on a parameter manifold ring S^1, which is introduced by performing a gauge transformation to the spin Hamiltonian through a twist operator. The cyclic ground-state quantum distance and the second derivative of the ground-state energy are studied in different exchange coupling parameter regions. Particularly, we show that, in the case of exchange coupling parameter J a = J b, the quantum ferromagnetic phase can be characterized by an invariant quantum distance and this distance will decay to zero rapidly in the paramagnetic phase.

Order Topology and Bi-Scott Topology on a Poset

In this paper, some properties of order topology and bi-Scott topology on a poset are obtained. Order-convergence in posets is further studied. Especially, a sufficient and necessary condition for order-convergence to be topological is given for some kind of posers.

Structure-controlled slow dynamics in Al−Mg melts

Molecular dynamics simulation was employed to investigate the dynamical and structural properties of Al−Mg melts with the Al concentration systematically changed.The results show that the viscosity of Al67Mg33 abnormally surpasses that of Al85Mg15 below 550 K,inconsistent with the tendency at high temperatures.The evolution of the icosahedral order population is found to account for this dynamic behavior.Structural analysis shows a preferred bonding between Al and Mg atoms in the nearest neighbor shells,while a repelling tendency between them in the second shells,leading to the prepeak emergence in the partial static structure factors.The formation of icosahedral clusters is constrained in the Al-rich compositions because of the lack of sufficient Mg atoms to stabilize the clusters geometrically.These results demonstrate the structural consequence through the interplay between geometric packing and chemical interaction.These findings are crucial to understanding the structure−dynamic properties in Al−Mg melts.

Categorical computation

In quantum computing, the computation is achieved by linear operators in or between Hilbert spaces. In this work, we explore a new computation scheme, in which the linear operators in quantum computing are replaced by (higher) functors between two (higher) categories. If from Turing computing to quantum computing is the first quantization of computation, then this new scheme can be viewed as the second quantization of computation. The fundamental problem in realizing this idea is how to realize a (higher) functor physically. We provide a theoretical idea of realizing (higher) functors physically based on the physics of topological orders.

Measures of Semi Noncompactness and Set Valued AM Mappings

In this paper we define measures of semi noncompactness in a locally convex topological linear space with respect to a given seminorm. Then we get a fixed point theorem for a class of condensing set valued mappings and apply it to differential inclusions.