Superconformal invariance in two dimensions and the tricritical Ising model

Friedan, Daniel; Qiu, Zhihai; Shenker, Stephen H.

doi:10.1016/0370-2693(85)90819-6

Cited by 448 publications

(275 citation statements)

References 22 publications

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“…The transition between the Z 2 phase and the Haldane gapped phase occurs at the angle θ 2,1 ≈ −0.19π, which shows little dependence on the level k. The critical point itself is described by a N = 1 superconformal minimal model 38 ,…”

Section: Superconformal Critical Pointmentioning

confidence: 98%

Anyonic quantum spin chains: Spin-1 generalizations and topological stability

et al. 2013

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There are many interesting parallels between systems of interacting non-Abelian anyons and quantum magnetism, occuring in ordinary SU(2) quantum magnets. Here we consider theories of so-called su(2) k anyons, well-known deformations of SU (2), in which only the first k + 1 angular momenta of SU(2) occur. In this manuscript, we discuss in particular anyonic generalizations of ordinary SU(2) spin chains with an emphasis on anyonic spin S = 1 chains. We find that the overall phase diagrams for these anyonic spin-1 chains closely mirror the phase diagram of the ordinary bilinear-biquadratic spin-1 chain including anyonic generalizations of the Haldane phase, the AKLT construction, and supersymmetric quantum critical points. A novel feature of the anyonic spin-1 chains is an additional topological symmetry that protects the gapless phases. Distinctions further arise in the form of an even/odd effect in the deformation parameter k when considering su(2) k anyonic theories with k ≥ 5, as well as for the special case of the su(2)4 theory for which the spin-1 representation plays a special role. We also address anyonic generalizations of spin-1/2 chains with a focus on the topological protection provided for their gapless ground states. Finally, we put our results into context of earlier generalizations of SU(2) quantum spin chains, in particular so-called (fused) Temperley-Lieb chains.

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Section: Superconformal Critical Pointmentioning

confidence: 98%

Anyonic quantum spin chains: Spin-1 generalizations and topological stability

et al. 2013

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“…The super-Virasoro algebra governs the superconformal invariance [20,24]. It plays in the supersymmetric context the same rôle that the Virasoro algebra plays in the local conformal case.…”

Section: Super-virasoro Algebramentioning

confidence: 99%

“…are studied in [20,24]; in the NS case they are irreducible and uniquely determined by the values of c and h. In the Ramond case one has to further specify the action of G 0 on the lowest energy subspace. It turns out that for a possible value of c and h there two inequivalent irreducible lowest weight representations (but for the case c = h/24 when the representation is unique and graded).…”

Section: Super-virasoro Algebramentioning

confidence: 99%

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Structure and Classification of Superconformal Nets

Carpi

Kawahigashi

Longo

2008

Ann. Henri Poincaré

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We study the general structure of Fermi conformal nets of von Neumann algebras on S 1 , consider a class of topological representations, the general representations, that we characterize as Neveu-Schwarz or Ramond representations, in particular a Jones index can be associated with each of them. We then consider a supersymmetric general representation associated with a Fermi modular net and give a formula involving the Fredholm index of the supercharge operator and the Jones index. We then consider the net associated with the super-Virasoro algebra and discuss its structure. If the central charge c belongs to the discrete series, this net is modular by the work of F. Xu and we get an example where our setting is verified by considering the Ramond irreducible representation with lowest weight c/24. We classify all the irreducible Fermi extensions of any super-Virasoro net in the discrete series, thus providing a classification of all superconformal nets with central charge less than 3/2.

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“…The coset (B.4) is found [20] to form the minimal models of the N = 1 superconformal algebra ( [21][22][23] and appendix B). The minimal models of the W N algebra [24] are the su(N) diagonal cosets…”

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confidence: 99%