Many-body systems with non-abelian statistics

Blok, B.; Wen, Xiao-Gang

doi:10.1016/0550-3213(92)90402-w

Cited by 112 publications

(189 citation statements)

References 39 publications

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“…In particular, one can build a hierarchy on the SU͑2͒ 2 ϫ U͑1͒ 2 NAF state 28 or similarly constructed states given by SO͑5͒ 1 ϫ U͑1͒ 2 or SO͑7͒ 1 ϫ U͑1͒ 2 . We note that Ising, SU͑2͒ 2 , SO͑5͒ 1 , and SO͑7͒ 1 all have the same fusion algebra and all have a fermionic field ͑the equivalent of the ͒ assigned to the electron in such states.…”

Section: Discussionmentioning

confidence: 99%

“…Aside from the Abelian hierarchy states, the non-Abelian Read-Rezayi ͑RR͒ k-body clustered states 26 ͑which include MR͒ and their particle-hole conjugates are essentially the only single layer spin-polarized descriptions that have been proposed for these FQH plateaus. There are also other proposed non-Abelian states, such as the SU͑N͒ k NAF ͑non-Abelian FQH͒ states 27,28 whose potential relevance to the second Landau level is largely unexplored. The experiments of Ref.…”

Section: Introductionmentioning

confidence: 99%

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Fractional quantum Hall hierarchy and the second Landau level

2008

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We generalize the fractional quantum Hall hierarchy picture to apply to arbitrary, possibly non-Abelian, fractional quantum Hall states. Applying this to the =5/ 2 Moore-Read state, we construct explicit trial wave functions to describe the fractional quantum Hall effect in the second Landau level. The resulting hierarchy of states, which reproduces the filling fractions of all observed Hall conductance plateaus in the second Landau level, is characterized by electron pairing in the ground state and an excitation spectrum that includes nonAbelian anyons of the Ising type. We propose this as a unifying picture in which p-wave pairing characterizes the fractional quantum Hall effect in the second Landau level.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fractional quantum Hall hierarchy and the second Landau level

2008

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“…Chern number for two dimensional systems) and Fubini-Study metric [4], the metric measuring the quantum distance. While non-zero integrated Berry curvature can lead to the existence of states that are protected against disorder [5][6][7] and to effects like quantized Hall conductance of a band insulator [8], non-zero Fubini Study metric can lead to phenomena such as pseudospin conservation laws in single layer graphene [4] and unusual features in the current noise spectrum of a band insulator [9]. Recently, a strong interest has emerged in flat band systems as playgrounds for investigating the interplay of strong correlation effects and non-trivial quantum geometry.…”

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confidence: 99%

Flat bands with Berry curvature in multilayer graphene

Kumar

Nandkishore

2013

Phys. Rev. B

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We demonstrate that flat bands with local Berry curvature arise naturally in chiral (ABC) multilayer graphene placed on a boron nitride (BN) substrate. The degree of flatness can be tuned by varying the number of graphene layers N . For N = 7 the bands become nearly flat, with a small bandwidth ∼ 3.6 meV. The two nearly flat bands coming from the K and K valleys cross along lines in the reduced zone. Weak intervalley tunneling turns the bandcrossing into an avoided crossing, producing two nearly flat bands with global Chern number zero, but with local Berry curvature. The flatness of the bands suggests that many body effects will dominate the physics, while the local Berry curvature of the bands endows the system with a nontrivial quantum geometry. The quantum geometry effects manifest themselves through the quantum distance (Fubini-Study) metric, rather than the more conventional Chern number. Multilayer graphene on BN thus provides a platform for investigating the effect of interactions in a system with a non-trivial quantum distance metric, without the complication of non-zero Chern numbers. We note in passing that flat bands with non-zero Chern number can also be realized by making use of magnetic adatoms, and explicitly breaking time reversal symmetry.

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“…For N ≥ 2, the particles carry both an internal isospin under SU(N ), and also a scale size. This results in a higher dimensional generalisation of a class of 2d non-Abelian Hall states, first discovered by Blok and Wen [16].…”

Section: Jhep04(2018)040mentioning

confidence: 99%

“…The ground state is then formed by building up consecutive baryons which minimize the value of l + m. This means that we first act with B † (0, 0), followed by [16]. In the 2d QHE, the Blok-Wen states are a particularly simple class of non-Abelian quantum Hall states.…”

Section: Jhep04(2018)040mentioning

confidence: 99%

ADHM and the 4d quantum Hall effect

Barns-Graham

Dorey

Lohitsiri

et al. 2018

J. High Energ. Phys.

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Yang-Mills instantons are solitonic particles in d = 4 + 1 dimensional gauge theories. We construct and analyse the quantum Hall states that arise when these particles are restricted to the lowest Landau level. We describe the ground state wavefunctions for both Abelian and non-Abelian quantum Hall states. Although our model is purely bosonic, we show that the excitations of this 4d quantum Hall state are governed by the Nekrasov partition function of a certain five dimensional supersymmetric gauge theory with Chern-Simons term. The partition function can also be interpreted as a variant of the Hilbert series of the instanton moduli space, counting holomorphic sections rather than holomorphic functions.It is known that the Hilbert series of the instanton moduli space can be rewritten using mirror symmetry of 3d gauge theories in terms of Coulomb branch variables. We generalise this approach to include the effect of a five dimensional Chern-Simons term. We demonstrate that the resulting Coulomb branch formula coincides with the corresponding Higgs branch Molien integral which, in turn, reproduces the standard formula for the Nekrasov partition function.

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Many-body systems with non-abelian statistics

Cited by 112 publications

References 39 publications

Fractional quantum Hall hierarchy and the second Landau level

Fractional quantum Hall hierarchy and the second Landau level

Flat bands with Berry curvature in multilayer graphene

ADHM and the 4d quantum Hall effect

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