Synthesis of Fe−C⋮C−M Complexes through Condensation of Fe−C⋮C−H with M−H or M−NMe<sub>2</sub>

Gu, Xinhong; Sponsler, Michael B.

doi:10.1021/om9800187

Cited by 39 publications

(45 citation statements)

References 19 publications

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“…Examples have been found in one 31 and two [32][33][34][35][36] dimensions where different free fermion SPT phases become the same with interactions. Moreover, new interacting SPT phases can exist which cannot be realized by free fermion systems.…”

Section: 30mentioning

confidence: 99%

Symmetry-Protected Topological Orders in Interacting Bosonic Systems

Chen

Liu

et al. 2012

Science

599

619

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Symmetry protected topological (SPT) states are bulk gapped states with gapless edge excitations protected by certain symmetries. The SPT phases in free fermion systems, like topological insulators, can be classified by the K-theory. However, it is not known what SPT phases exist in general interacting systems. In this paper, we present a systematic way to construct SPT phases in interacting bosonic systems, which allows us to identify many new SPT phases, including three bosonic versions of topological insulators in three dimension and one in two dimension protected by particle number conservation and time reversal symmetry. Just as group theory allows us to construct 230 crystal structures in 3D, we find that group cohomology theory allows us to construct different interacting bosonic SPT phases in any dimensions and for any symmetry groups. In particular, we are going to show how topological terms in the path integral description of the system can be constructed from nontrivial group cohomology classes, giving rise to exactly soluble Hamiltonians, explicit ground state wave functions and symmetry protected gapless edge excitations. We used to believe that different phases of matter are different because they have different symmetries.1-3 Recently, we see a deep connection between quantum phases and quantum entanglement 4-6 which allows us to go beyond this framework. First it was realized that even in systems without any symmetry there can be distinct quantum phases -topological phases 7,8 due to different patterns of long-range entanglement in the states.6 For systems with symmetries, difference in long-range entanglement and in symmetry still lead to distinct phases. Moreover, even short-range entangled states with the same symmetry can belong to different phases. These symmetric short-range entangled states are said to contain a new kind of order -symmetry protected topological (SPT) order.9 The SPT phases have symmetry protected gapless edge modes despite the bulk gap, which clearly indicates the topological nature of this order. On the other hand, the gapless edge modes disappear when the symmetry of the system is broken, indicating that this is a different type of topological order than that found in fractional quantum Hall systems 10,11 whose edge modes cannot be removed with any local perturbation. 12Also, SPT orders have no factional statistics or fractional charges, while intrinsic topological orders from long range entanglement can have them. The discovery of SPT order hence greatly expands our original understanding of possible phases in many-body systems.One central issue is to understand what SPT phases exist and much progress has been made in this regard. The first system with SPT order was discovered decades ago in spin-1 Haldane chains. The Haldane chain with antiferromagnetic interactions was shown to have a gapped bulk 13,14 and degenerate modes at the ends of the chain 15-17 which are protected by spin rotation or time reversal symmetry of the system.9,18 This model has been generalized, l...

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Section: 30mentioning

confidence: 99%

Symmetry-Protected Topological Orders in Interacting Bosonic Systems

Chen

Liu

et al. 2012

Science

599

619

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“…If the HBK system is Painlevé integrable, the resonance conditions at = 1 2 3 3 4 4 5 must be satisfied identically such that the seven arbitrary functions among the can be introduced into the general series expansions (4). For = 1, we can easily obtain from (7) - (9) 1 = 1 = (11) while 1 is an arbitrary function.…”

Section: Painlevé Property Of 2+1-dimensional Hbk Systemmentioning

confidence: 99%

“…Many methods have been established by mathematicians and physicists to study the integrability of NPDE's. Some of the most important methods are the inverse scattering method(IST) [1], the bilinear method [2], the symmetry reductions [3], Bäcklund and Darboux transformations [4], the Painlevé analysis method [5], etc. As known, a model which is integrable in one sense may not be integrable in another sense.…”

Section: Introductionmentioning

confidence: 99%

Painlevé Integrability and Abundant Localized Structures of (2+1)-dimensional Higher Order Broer-Kaup System

Lin

2002

Zeitschrift Für Naturforschung A

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It is proven that the (2+1) dimensional higher-order Broer-Kaup system the possesses the Painlevé property, using the Weiss-Tabor-Carnevale method and Kruskal's simplification. Abundant localized coherent structures are obtained by using the standard truncated Painlevé expansion and the variable separation method. Fractal dromion solutions and multi-peakon structures are discussed. The interactions of three peakons are investigated. The interactions among the peakons are not elastic; they interchange their shapes but there is no phase shift.

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“…Hydrozirconation reactions were also observed with the vinyl and acetylenic ferrocenyl complexes [227]. In marked contrast, the iron complex Cp*(dppe)Fe-C≡CH reacts anomalously with Schwartz's reagent to form acetylide C 2 -bridged heterodinuclear complexes (Scheme 8-31) [228]. CO 2 -Bridged bimetallic zirconocene complexes have been formed from 1 and metallocarboxylic acids [229].…”

Section: Bimetallic Transition Metal-zirconocene Complexes From Zircomentioning

confidence: 99%

Hydrozirconation

Igau¹

2001

Catalytic Heterofunctionalization

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Synthesis of Fe−C⋮C−M Complexes through Condensation of Fe−C⋮C−H with M−H or M−NMe₂

Cited by 39 publications

References 19 publications

Symmetry-Protected Topological Orders in Interacting Bosonic Systems

Symmetry-Protected Topological Orders in Interacting Bosonic Systems

Painlevé Integrability and Abundant Localized Structures of (2+1)-dimensional Higher Order Broer-Kaup System

Hydrozirconation

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Synthesis of Fe−C⋮C−M Complexes through Condensation of Fe−C⋮C−H with M−H or M−NMe2

Cited by 39 publications

References 19 publications

Symmetry-Protected Topological Orders in Interacting Bosonic Systems

Symmetry-Protected Topological Orders in Interacting Bosonic Systems

Painlevé Integrability and Abundant Localized Structures of (2+1)-dimensional Higher Order Broer-Kaup System

Hydrozirconation

Contact Info

Product

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Synthesis of Fe−C⋮C−M Complexes through Condensation of Fe−C⋮C−H with M−H or M−NMe₂