We classify condensable𝐸E_(2)-algebras in a modular tensor category C up to 2-Morita equivalence.Physically,this classification provides an explicit criterion to determine when distinct condensable𝐸E_(...We classify condensable𝐸E_(2)-algebras in a modular tensor category C up to 2-Morita equivalence.Physically,this classification provides an explicit criterion to determine when distinct condensable𝐸E_(2)-algebras yield the same condensed topological phase under a two-dimensional anyon condensation process.The relations between different condensable algebras can be translated into their module categories,interpreted physically as gapped domain walls in topological orders.As concrete examples,we interpret the categories of quantum doubles of finite groups and examples beyond group symmetries.Our framework fully elucidates the interplay among condensable𝐸E_(1)-algebras in C,condensable𝐸E_(2)-algebras in C up to 2-Morita equivalence,and Lagrangian algebras in C⊠C.展开更多
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 i...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.展开更多
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...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？展开更多
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.
Higher-order band topology not only enriches our understanding of topological phases but also unveils pioneering lower-dimensional boundary states,which harbors substantial potential for next-generation device applica...Higher-order band topology not only enriches our understanding of topological phases but also unveils pioneering lower-dimensional boundary states,which harbors substantial potential for next-generation device applications.The distinct electronic configurations and tunable attributes of two-dimensional materials position them as a quintessential platform for the realization of second-order topological insulators(SOTIs).This article provides an overview of the research progress in SOTIs within the field of two-dimensional electronic materials,focusing on the characterization of higher-order topological properties and the numerous candidate materials proposed in theoretical studies.These endeavors not only enhance our understanding of higher-order topological states but also highlight potential material systems that could be experimentally realized.展开更多
Higher-order topological insulators,which host topologically protected states at boundaries that are at least two dimensions lower than the bulk,are an emerging class of topological materials.They provide great opport...Higher-order topological insulators,which host topologically protected states at boundaries that are at least two dimensions lower than the bulk,are an emerging class of topological materials.They provide great opportunities for exploring novel topological phenomena and fascinating applications.Utilizing a low-temperature scanning tunneling microscope,we construct breathing-kagome lattices with Fe adatoms on Ag(111)and investigate their electronic properties.We observe the higher-order topological boundary states in the topological phase but not in the trivial one,which is consistent with the theory.These states are found to be robust against the removal of bulk or edge adatoms.Further,we show the arbitrary positioning of these states either at corner,edge,or bulk sites by slightly modifying their neighbors.Our study not only demonstrates the formation and robustness of the electronic higher-order topological boundary states in real atomic systems but also provides a route for controlling their positions.展开更多
In conventional higher-order topological insulators(HOTIs),the emergence of topological states can be explained by using the nonzero bulk polarization index.However,corner states emerge in HOTIs with incomplete bounda...In conventional higher-order topological insulators(HOTIs),the emergence of topological states can be explained by using the nonzero bulk polarization index.However,corner states emerge in HOTIs with incomplete boundary unit cells(i.e.,boundary defects)even though the bulk polarization is zero,which challenges the conventional understanding of HOTIs.Here,based on a Kekul´e-distorted honeycomb lattice with incomplete unit cells,we reveal that incomplete unit cells exhibit fractional charges through the analysis of Wannier centers by developing a compensation method and creating the concept of Wannier center domain(WCD)which is the smallest region that one Wannier center occupies.This method compensates for the missing parts of these boundary incomplete unit cells with additional WCDs to make them complete.The compensated WCDs automatically carry the corresponding charge,and this charge together with that of the incomplete unit cell constitutes the total charge of the complete unit cell after compensation.We conclude that the emergence of corner states is attributed to the filling anomaly,which is a fundamental mechanism.Our results refresh the understanding of HOTIs,especially those with structural discontinuities,and provide a novel design for topological states which have application value in producing optical functional devices.展开更多
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...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.展开更多
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 M...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.展开更多
We propose the superconducting van der Waals material 4Hb-TaS_(2)to realize the Z_(2)topological order and interpret the recent discovery of the spontaneous vortex generation in 4Hb-TaS_(2)as the vison-vortex nucleati...We propose the superconducting van der Waals material 4Hb-TaS_(2)to realize the Z_(2)topological order and interpret the recent discovery of the spontaneous vortex generation in 4Hb-TaS_(2)as the vison-vortex nucleation.For the alternating stacking of metallic/superconducting and Mott insulating layers in 4Hb-TaS_(2),we expect the local moments in the Mott insulating 1T-TaS_(2)layer to form the Z_(2)topological order.The spontaneous vortex generation in 4Hb-TaS_(2)is interpreted from the transition or nucleation between the superconducting vortex and the Z_(2)vison in different phase regimes.Differing from the single vison-vortex nucleation in the original Senthil-Fisher’s cuprate proposal,we consider such nucleation process between the superconducting vortex lattice and the vison crystal.We further propose experiments to distinguish this proposal with the Z_(2)topological order from the chiral spin liquid scenarios.展开更多
Intrinsic higher-order topological insulators driven solely by orbital coupling are rare in electronic materials.Here,we propose that monolayer LaBrO is an intrinsic two-dimensional second-order topological insulator....Intrinsic higher-order topological insulators driven solely by orbital coupling are rare in electronic materials.Here,we propose that monolayer LaBrO is an intrinsic two-dimensional second-order topological insulator.The generalized second-order topological phase arises from the coupling between the 5d orbital of the La atom and the 2p orbital of the O atom.The underlying physics can be thoroughly described by a four-band generalized higher-order topological model.Notably,the edge states and corner states of monolayer LaBrO exhibit different characteristics in terms of morphology,number,and location distribution under different boundary and nanocluster configurations.Furthermore,the higher-order topological corner states of monolayer LaBrO are robust against variations in spin-orbit coupling and different values of Hubbard U.This provides a material platform for studying intrinsic 2D second-order topological insulators.展开更多
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 ...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.展开更多
In the paper [Monotone countable paracompactness and maps to ordered topological vector spaces, Top. Appl., 2014, 169（3）： 51–70], Yamazaki initiated the study on maps with values into ordered topological vector sp...In the paper [Monotone countable paracompactness and maps to ordered topological vector spaces, Top. Appl., 2014, 169（3）： 51–70], Yamazaki initiated the study on maps with values into ordered topological vector spaces. Characterizations of monotonically countably paracompact spaces and some other spaces in terms of maps to ordered topological vector spaces were obtained. In this paper, following Yamazaki＇s method, we present some characterizations of stratifiable spaces and k-semi-stratifiable spaces in terms of maps with values into ordered topological vector spaces.展开更多
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...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.展开更多
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-ener...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.展开更多
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 transform...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.展开更多
In this paper, some characterizations of pairwise semi-stratifiable spaces are given by means of pairwise g-functions and semi-continuous functions and the pairwise semi-stratifiability of topological ordered C-spaces...In this paper, some characterizations of pairwise semi-stratifiable spaces are given by means of pairwise g-functions and semi-continuous functions and the pairwise semi-stratifiability of topological ordered C-spaces with semi-stratifiable topology is discussed.展开更多
Higher-order topological insulators(HOTIs)can support boundary states at least two dimensions lower than the bulk,attracting intensive attention from both fundamental science and application sides.Lattice-based tight-...Higher-order topological insulators(HOTIs)can support boundary states at least two dimensions lower than the bulk,attracting intensive attention from both fundamental science and application sides.Lattice-based tight-binding models such as Benalcazar-Bernevig-Hughes model have driven significant advancements in realizing HOTIs across various physical systems.Here,beyond lattice model,we demonstrate that a cylinder with an arbitrary cross section,composed of a homogeneous electromagnetic medium featuring nontrivial second Chern numbers c_(2)=±1 in a synthetic five-dimensional space,can exhibit topologically protected HOTI-type hinge states in three-dimensional laboratory space.Interestingly,this hinge state is essentially a chiral zero mode arising from the interaction between Weyl arc surface states,guaranteed by a nontrivial c_(2),and an effective magnetic field induced by the curvature of the cylinder surface.Compared to conventional schemes to generate HOTIs,our approach is more robust,as it is an intrinsic topological phase and therefore does not rely on additional symmetry protections such as time-reversal,parity,or chiral symmetry.We experimentally realize such a cylinder using a photonic metamaterial and confirm the existence of hinge states via microwave near-field measurements.Our work introduces the concept of boundary gauge fields and establishes the link between synthetic-space c_(2) and real-space HOTI states,thereby generalizing HOTIs to cornerless systems.展开更多
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...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.展开更多
Topological orders are a class of exotic states of matter characterized by patterns of long-range entanglement.Certain topologically ordered systems are proposed as potential realization of fault-tolerant quantum comp...Topological orders are a class of exotic states of matter characterized by patterns of long-range entanglement.Certain topologically ordered systems are proposed as potential realization of fault-tolerant quantum computation.Topological orders can arise in two-dimensional spin-lattice models.In this paper,we engineer a time-dependent Hamiltonian to prepare a topologically ordered state through adiabatic evolution.The other sectors in the degenerate ground-state space of the model are obtained by applying nontrivial operations corresponding to closed string operators.Each sector is highly entangled,as shown from the completely reconstructed density matrices.This paves the way towards exploring the properties of topological orders and the application of topological orders in topological quantum memory.展开更多
基金supported by Research Grants Council(RGC),University Grants Committee(UGC)of Hong Kong(ECS No.24304722)。
文摘We classify condensable𝐸E_(2)-algebras in a modular tensor category C up to 2-Morita equivalence.Physically,this classification provides an explicit criterion to determine when distinct condensable𝐸E_(2)-algebras yield the same condensed topological phase under a two-dimensional anyon condensation process.The relations between different condensable algebras can be translated into their module categories,interpreted physically as gapped domain walls in topological orders.As concrete examples,we interpret the categories of quantum doubles of finite groups and examples beyond group symmetries.Our framework fully elucidates the interplay among condensable𝐸E_(1)-algebras in C,condensable𝐸E_(2)-algebras in C up to 2-Morita equivalence,and Lagrangian algebras in C⊠C.
文摘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.
文摘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？
基金The project is supported by the NNSF of China(No.10971185,10971186)Fujian Province support college research plan project(No.JK2011031)
文摘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.
基金supported by the National Natu-ral Science Foundation of China(Grants No.12174220 and No.12074217)the Shandong Provincial Science Foundation for Excellent Young Scholars(Grant No.ZR2023YQ001)+1 种基金the Taishan Young Scholar Program of Shandong Provincethe Qilu Young Scholar Pro-gram of Shandong University.
文摘Higher-order band topology not only enriches our understanding of topological phases but also unveils pioneering lower-dimensional boundary states,which harbors substantial potential for next-generation device applications.The distinct electronic configurations and tunable attributes of two-dimensional materials position them as a quintessential platform for the realization of second-order topological insulators(SOTIs).This article provides an overview of the research progress in SOTIs within the field of two-dimensional electronic materials,focusing on the characterization of higher-order topological properties and the numerous candidate materials proposed in theoretical studies.These endeavors not only enhance our understanding of higher-order topological states but also highlight potential material systems that could be experimentally realized.
基金supported by the National Key R&D Program of China(Grant Nos.2024YFA140850,2022YFA1403601,and 2023YFC2410501)the National Natural Science Foundation of China(Grants Nos.12241402,12474059,12274203,12374113,and 12274204)。
文摘Higher-order topological insulators,which host topologically protected states at boundaries that are at least two dimensions lower than the bulk,are an emerging class of topological materials.They provide great opportunities for exploring novel topological phenomena and fascinating applications.Utilizing a low-temperature scanning tunneling microscope,we construct breathing-kagome lattices with Fe adatoms on Ag(111)and investigate their electronic properties.We observe the higher-order topological boundary states in the topological phase but not in the trivial one,which is consistent with the theory.These states are found to be robust against the removal of bulk or edge adatoms.Further,we show the arbitrary positioning of these states either at corner,edge,or bulk sites by slightly modifying their neighbors.Our study not only demonstrates the formation and robustness of the electronic higher-order topological boundary states in real atomic systems but also provides a route for controlling their positions.
基金supported by the Natural Science Basic Research Program of Shaanxi Province (Grant Nos.2024JC-JCQN-06 and2025JC-QYCX-006)the National Natural Science Foundation of China (Grant No.12474337)Chinese Academy of Sciences Project (Grant Nos.E4BA270100,E4Z127010F,E4Z6270100,and E53327020D)。
文摘In conventional higher-order topological insulators(HOTIs),the emergence of topological states can be explained by using the nonzero bulk polarization index.However,corner states emerge in HOTIs with incomplete boundary unit cells(i.e.,boundary defects)even though the bulk polarization is zero,which challenges the conventional understanding of HOTIs.Here,based on a Kekul´e-distorted honeycomb lattice with incomplete unit cells,we reveal that incomplete unit cells exhibit fractional charges through the analysis of Wannier centers by developing a compensation method and creating the concept of Wannier center domain(WCD)which is the smallest region that one Wannier center occupies.This method compensates for the missing parts of these boundary incomplete unit cells with additional WCDs to make them complete.The compensated WCDs automatically carry the corresponding charge,and this charge together with that of the incomplete unit cell constitutes the total charge of the complete unit cell after compensation.We conclude that the emergence of corner states is attributed to the filling anomaly,which is a fundamental mechanism.Our results refresh the understanding of HOTIs,especially those with structural discontinuities,and provide a novel design for topological states which have application value in producing optical functional devices.
文摘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.
文摘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.
基金supported by the Ministry of Science and Technology of China with Grants No.2021YFA1400300the National Science Foundation of China with Grant No.92065203by the Fundamental Research Funds for the Central Universities,Peking University.
文摘We propose the superconducting van der Waals material 4Hb-TaS_(2)to realize the Z_(2)topological order and interpret the recent discovery of the spontaneous vortex generation in 4Hb-TaS_(2)as the vison-vortex nucleation.For the alternating stacking of metallic/superconducting and Mott insulating layers in 4Hb-TaS_(2),we expect the local moments in the Mott insulating 1T-TaS_(2)layer to form the Z_(2)topological order.The spontaneous vortex generation in 4Hb-TaS_(2)is interpreted from the transition or nucleation between the superconducting vortex and the Z_(2)vison in different phase regimes.Differing from the single vison-vortex nucleation in the original Senthil-Fisher’s cuprate proposal,we consider such nucleation process between the superconducting vortex lattice and the vison crystal.We further propose experiments to distinguish this proposal with the Z_(2)topological order from the chiral spin liquid scenarios.
基金financially supported by the National Key R&D Program of China(Grant No.2022YFA1403200)the National Natural Science Foundation of China(Grant Nos.92265104,12022413,and 11674331)+5 种基金the Basic Research Program of the Chinese Academy of Sciences Based on Major Scientific Infrastructures(Grant No.JZHKYPT-2021-08)the CASHIPS Director’s Fund(Grant No.BJPY2023A09)the“Strategic Priority Research Program(B)”of the Chinese Academy of Sciences(Grant No.XDB33030100)Anhui Provincial Major S&T Project(Grant No.s202305a12020005)the Major Basic Program of Natural Science Foundation of Shandong Province(Grant No.ZR2021ZD01)the High Magnetic Field Laboratory of Anhui Province(Grant No.AHHM-FX-2020-02)。
文摘Intrinsic higher-order topological insulators driven solely by orbital coupling are rare in electronic materials.Here,we propose that monolayer LaBrO is an intrinsic two-dimensional second-order topological insulator.The generalized second-order topological phase arises from the coupling between the 5d orbital of the La atom and the 2p orbital of the O atom.The underlying physics can be thoroughly described by a four-band generalized higher-order topological model.Notably,the edge states and corner states of monolayer LaBrO exhibit different characteristics in terms of morphology,number,and location distribution under different boundary and nanocluster configurations.Furthermore,the higher-order topological corner states of monolayer LaBrO are robust against variations in spin-orbit coupling and different values of Hubbard U.This provides a material platform for studying intrinsic 2D second-order topological insulators.
文摘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.
基金Supported by the National Natural Science Foundation of China(Grant No.11401262)
文摘In the paper [Monotone countable paracompactness and maps to ordered topological vector spaces, Top. Appl., 2014, 169（3）： 51–70], Yamazaki initiated the study on maps with values into ordered topological vector spaces. Characterizations of monotonically countably paracompact spaces and some other spaces in terms of maps to ordered topological vector spaces were obtained. In this paper, following Yamazaki＇s method, we present some characterizations of stratifiable spaces and k-semi-stratifiable spaces in terms of maps with values into ordered topological vector spaces.
基金supported by Key R&D project of Zhejiang Province (2018C01005),http://kjt.zj.gov.cn/.
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11804107)。
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11404023 and 11347131)
文摘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.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1097118510971186+3 种基金11201414)Fujian Province Support College Research Plan Project(Grant No.JK2011031)the Natural Science Foundation of Fujian Province(Grant Nos.2012J050132013J01029)
文摘In this paper, some characterizations of pairwise semi-stratifiable spaces are given by means of pairwise g-functions and semi-continuous functions and the pairwise semi-stratifiability of topological ordered C-spaces with semi-stratifiable topology is discussed.
基金supported by National Key Research and Development Program of China(Grants No.2023YFA1407700,2023YFA1406901)National Natural Science Foundation China(Grants No.12374343)+2 种基金the start-up funding of Fudan University(JIH1232133Y)the New Cornerstone Science Foundation,the Research Grants Council of Hong Kong(AoE/P-502/20,STG3/E-704/23-N,17309021)Guangdong Provincial Quantum Science Strategic Initiative(GDZX2204004,GDZX2304001).
文摘Higher-order topological insulators(HOTIs)can support boundary states at least two dimensions lower than the bulk,attracting intensive attention from both fundamental science and application sides.Lattice-based tight-binding models such as Benalcazar-Bernevig-Hughes model have driven significant advancements in realizing HOTIs across various physical systems.Here,beyond lattice model,we demonstrate that a cylinder with an arbitrary cross section,composed of a homogeneous electromagnetic medium featuring nontrivial second Chern numbers c_(2)=±1 in a synthetic five-dimensional space,can exhibit topologically protected HOTI-type hinge states in three-dimensional laboratory space.Interestingly,this hinge state is essentially a chiral zero mode arising from the interaction between Weyl arc surface states,guaranteed by a nontrivial c_(2),and an effective magnetic field induced by the curvature of the cylinder surface.Compared to conventional schemes to generate HOTIs,our approach is more robust,as it is an intrinsic topological phase and therefore does not rely on additional symmetry protections such as time-reversal,parity,or chiral symmetry.We experimentally realize such a cylinder using a photonic metamaterial and confirm the existence of hinge states via microwave near-field measurements.Our work introduces the concept of boundary gauge fields and establishes the link between synthetic-space c_(2) and real-space HOTI states,thereby generalizing HOTIs to cornerless systems.
文摘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.
基金supported by the National Program on Key Basic Research Project(Grant Nos.2013CB921800,and 2014CB848700)the National Science Fund for Distinguished Young Scholars(Grant No.11425523)+4 种基金the National Natural Science Foundation of China(Grant Nos.11805008,11227901,11734002,11374032,and 91021005)the Strategic Priority Research Program(B)of the CAS(Grant No.XDB01030400)the Research Fund for the Doctoral Program of Higher Education of China(RFDPHEC)(Grant No.20113402110044)the support from the John Templeton foundation(Grant No.39901)supported in part by Perimeter Institute for Theoretical Physics
文摘Topological orders are a class of exotic states of matter characterized by patterns of long-range entanglement.Certain topologically ordered systems are proposed as potential realization of fault-tolerant quantum computation.Topological orders can arise in two-dimensional spin-lattice models.In this paper,we engineer a time-dependent Hamiltonian to prepare a topologically ordered state through adiabatic evolution.The other sectors in the degenerate ground-state space of the model are obtained by applying nontrivial operations corresponding to closed string operators.Each sector is highly entangled,as shown from the completely reconstructed density matrices.This paves the way towards exploring the properties of topological orders and the application of topological orders in topological quantum memory.
