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Variational Corner Transfer Matrix Renormalization Group Method for Classical Statistical Models

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Chinese Physics Letters 2022年第6期39卷 65-70页

作者： x.f.liu Y.f.fu W.Q.Yu J.f.Yu Z.Y.xie Department of Physics Renmin University of ChinaBeijing 100872China School of Physics and Electronics Hunan UniversityChangsha 410082China

In the context of tensor network states,we for the first time reformulate the corner transfer matrix renormalization group(CTMRG)method into a variational bilevel optimization *** solution of the optimization problem corresponds to the fixed-point environment pursued in the conventional CTMRG method,from which the partition function of a classical statistical model,represented by an infinite tensor network,can be efficiently *** validity of this variational idea is demonstrated by the high-precision calculation of the residual entropy of the dimer model,and is further verified by investigating several typical phase transitions in classical spin models,where the obtained critical points and critical exponents all agree with the best known results in *** extension to three-dimensional tensor networks or quantum lattice models is straightforward,as also discussed briefly.

关键词： tensor variational straight

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STUDY Of THE NUCLEATION MECHANISM Of α-Al GRAINS AfTER ADDITION Of Al-Ti-B MASTER ALLOYS

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Acta Metallurgica Sinica(English Letters) 1998年第3期11卷 157-162页

作者： x.f.liu x.f.Bian x.G.Qi M.Thompson J.JMa

Nucleation sites of α-Al grains after addition of an Al-Ti-B master alloy into pure aluminium have been investigated using EPMA. The results show that either TiAl3 or boride particales can nucleate α-Al grains. But the number of TiAl3 nucleants is reduced with the holding time prolonged and the boride-nuclei are increasing gradually. Based on these results, a new refining method, adding molten Al-Ti-B into commercially pure aluminium, which has a quicker and better refining efficiency is presented.

关键词： Al-Ti-B master alloy grain refinement nucleation mechanism,α-Al nucleant

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Complete Band Gaps in Sandwich Phononic Crystal Plates

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Complete Band Gaps in Sandwich Phononic Crystal Plates

The 16th Annual Conference of Hong Kong Society of Theoretical and Applied Mechanics 2012、The 1st Mainland-Hong Kong Youth forum on Mechanics 2012、The 8th Shanghai-Hong Kong forum on Mechanics and Its Application 2012

作者： x.f.liu Y.S.Wang Institute of Engineering Mechanics Beijing Jiaotong University

Using the finite element method,the propagation of Lamb waves in sandwich phononic crystal plates(SPCP) is *** structure is composed of a two-dimensional phononic crystal plate coated with two substrates on both *** phononic crystal plate(PCP) is constituted by a square array of gold cylinders arranged in an epoxy matrix,and the substrates are made of *** is evidenced that some complete phononic band gaps(PBGs) are opened up by changing the thickness of PCP,and the width of the first PBG becomes larger as the thickness *** influence of substrates' thickness and material on the width of PBG is discussed as *** to the results,one can notice that the thickness of PCP and substrates plays a key role in tuning the band gaps of the SPCPs,and could estimate the best configuration of these two parameters in the application of vibration control and noise reduction.

关键词： Sandwich Complete Band Gaps in Sandwich Phononic Crystal Plates

The Applications of Ultralight Three-dimensional Graphene Networks in Electromagnetic Wave Absorption and Electro-active Shape Memory Composite

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The Applications of Ultralight Three-dimensional Graphene Ne...

第二届海峡两岸功能材料科技与产业峰会（2015）

作者： x.f.liu W.W.liu H.LI H.Z.liu State Key Laboratory of Metal Matrix Composites School of Materials Science and EngineeringShanghai Jiao Tong University

Thermally reduced graphene networks(TRGN)with low densities,less than 10 mg/cm-3,were synthesized by thermal reduction of graphene oxide/poly(vinyl alcohol)*** evaluate the electromagnetic wave absorption properties of TRGN,TRGN were nondestructively backfilled with wax via a vacuum-assisted *** as-prepared TRGN/wax composites,using integrated TRGN as fillers rather than directly dispersing

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Morphology-dependent photoluminescence and magnetism of Co:ZnS nanostructures

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Morphology-dependent photoluminescence and magnetism of Co:Z...

2012中国功能新材料学术论坛暨第三届全国电磁材料及器件学术会议

作者： x.f.liu~*,N.Yang and R.H.Yu~* School of Materials Science and Engineering,Beihang University,Beijing 100191,China

Co:ZnS nanostructures,in which Co ions are incorporated into ZnS lattice by replacing Zn sites, have been synthesized by simple solvothermal methods using mixed solvents of water and *** modifying the amount of ethylenediamine in solvent,quasi-spherical shape with different dispersity and nanorod shape Co:ZnS nanostructures are obtained,which possess visible photoluminescence and intrinsic *** is observed that the photoluminescence and ferromagnetism of the Co:ZnS nanostructures are closely related to the *** spectra of the Co:ZnS nanostructures exhibit strong multiple emission peaks involving different defect-related luminescence *** intensity of the emission peaks strongly depends on the amount of structural defects in nanostructures with different ***,the observed ferromagnetism varies with the morphologies of the nanostructures,which can be attributed to the change in the number of structural *** magnetic polaron mechanism is adopted to explain the mechanism of the intrinsic ferromagnetism in this system.

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Structure,photoluminesecent and magnetic properties of Co-doped ZnS nanocrystals

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Structure,photoluminesecent and magnetic properties of Co-do...

2012中国功能新材料学术论坛暨第三届全国电磁材料及器件学术会议

作者： N.Yang~*,x.f.liu,B.Yang,M.Zeng,J.x.Bao,L.Zhang,H.Z.Yang and R.H.Yu~* School of Materials Science and Engineering,Beihang University,Beijing 100191,China

Diluted magnetic semiconductors(DMSs)are of great interest due to their potential applications in spintronic devices that operate not only with electron charge but also utilize the electron spin as an additional degre...

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Gas Source Molecular Beam Epitaxy of High-Quality Strained Si1-xGex/Si Superlatice Materilas

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电子显微学报 1997年第4期 39-40页

作者： L.f.Zou\ Z.G.Wang\ D.Z.Sun\ x.f.liu\ J.W.Zhang J.P.Li\ M.Y.Kong\ L.Y.Lin (Laboratory of Semiconductor Materials Science, Institute of Semiconductors Chinese Academy of Sciences, P.O.Box 912, Beijing 100083, China)

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关键词： Source Gas Molecular High-Quality Strained Materilas Superlatice x)Ge_x/Si Beam Ge

Gas Source Molecular Beam Epitaxy of High-Quality Strained Si1-xGex/Si Superlattice Materilas

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Gas Source Molecular Beam Epitaxy of High-Quality Strained S...

1996年中国青年学者物理学讨论会

作者： L.f.Zou Z.G.Wang D.Z.Sun x.f.liu J.W.Zhang J.P.Li M.Y.Kong L.Y.Lin(Laboratory of Semiconductor Materials Science,Institute of Semiconductors Chinese Academy of Sciences,P.O.Box 912,Beijing 100083,China)

Gas source molecular beam epitaxy(GSMBE)has been used to grow SiGe alloys and SiGe/Si multi-quantum wells(MQWs)on(100)Si substrates with SiH and GeH as ***-crystalline epilayers with Ge composition as high as 43% have been produced at 620℃.Hetemstructures and MQWs with mirror-like surface morphology,good crystalline quality,and abrupt interfaces are demonstrated. Growth parameters,growth modes,and the structural characteristics have been studied by a variety of in situ and ex situ techniques.N-type doping was carried out using PH as dopant and maximum electron concentration of 6×10cm in Si epilayer was ***,p-type doping using BH was carried out and maximum hole concentrastion of 6.8×10cm in Si epilayer was successfully achieved.

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Edge supercurrent in Josephson junctions based on topological materials

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Science China(Physics,Mechanics & Astronomy) 2025年第2期Mechanics & Astronomy) .卷 5-16页

作者： Junjie Qi Chui-Zhen Chen Juntao Song Jie liu Ke He Qing-feng Sun x.C.xie Beijing Academy of Quantum Information Sciences School of Physical Science and Technology Soochow University Institute for Advanced Study Soochow University College of Physics and Hebei Advanced Thin films Laboratory Hebei Normal University School of Physics Xi'an Jiaotong UniversityMinistry of Education Key Laboratory for Non-Equilibrium Synthesis and Modulation of Condensed Matter State Key Laboratory of Low Dimensional Quantum Physics Department of PhysicsTsinghua University frontier Science Center for Quantum Information Hefei National Laboratory International Center for Quantum Materials School of PhysicsPeking University Interdisciplinary Center for Theoretical Physics and Information Sciences Fudan University

The interplay between novel topological states and superconductivity has garnered substantial interest due to its potential for topological quantum computing. The Josephson effect serves as a useful probe for edge superconductivity in these hybrid topological materials. In Josephson junctions based on topological materials, supercurrents exhibit unique quantum interference patterns,including the conventional fraunhofer oscillations, the Φ0-periodic oscillation, and the 2Φ0-periodic oscillation in response to the external magnetic field（Φ0=h/2e is the flux quantum, h the Planck constant, and e the electron charge）. These interference patterns stem from varied Andreev reflection mechanisms and the associated current density profiles. This review seeks to comprehensively examine the theoretical and experimental advancements in understanding the quantum interference patterns of edge supercurrents in Josephson junctions based on quantum spin Hall, quantum Hall, and quantum anomalous Hall systems.

关键词： quantum Hall effect quantum spin Hall effect quantum anomalous Hall effect Josephson junction edge supercurrent Andreev reflection