Statistics of Two-Dimensional Lattices with Four Components

Ashkin, J.; Teller, Edward

doi:10.1103/physrev.64.178

Cited by 594 publications

(418 citation statements)

References 1 publication

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“…We note that the su(2) 4 anyonic spin-1 chain has some similarities with the one-dimensional quantum Ashkin-Teller model 43 . The one-dimensional quantum Ashkin-Teller model, which is an anisotropic version of the two-dimensional Ashkin-Teller model 44 , also has a line of critical points on its self-dual line, realizing the orbifold CFTs with p = 1, 2, 3, 4, in addition to two gapped phases, one of which has a Z 2 sub-lattice structure.…”

Section: The Location Of the Phase Boundariesmentioning

confidence: 99%

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: The Location Of the Phase Boundariesmentioning

confidence: 99%

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

et al. 2013

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“…The Z 4 spin model (1) is a representation of the AT model [19]. An equivalent (and more standard) representation of the AT model is in terms of two coupled Ising models.…”

Section: The Modelmentioning

confidence: 99%

Critical interfaces of the Ashkin–Teller model at the parafermionic point

Picco¹,

Santachiara²

2010

J. Stat. Mech.

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We present an extensive study of interfaces defined in the Z 4 spin lattice representation of the Ashkin-Teller (AT) model. In particular, we numerically compute the fractal dimensions of boundary and bulk interfaces at the Fateev-Zamolodchikov point. This point is a special point on the self-dual critical line of the AT model and it is described in the continuum limit by the Z 4 parafermionic theory. Extending on previous analytical and numerical studies [10,12], we point out the existence of three different values of fractal dimensions which characterize different kind of interfaces. We argue that this result may be related to the classification of primary operators of the parafermionic algebra. The scenario emerging from the studies presented here is expected to unveil general aspects of geometrical objects of critical AT model, and thus of c = 1 critical theories in general.

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“…• The boundary critical Ashkin-Teller model In two dimensions, the Ashkin-Teller model [60] corresponds to two Ising models coupled by a local four spin interaction. The action associated with the critical line of the Ashkin-Teller (Z 4 ) model in the bulk corresponds to a conformal field theory with central charge c = 1 (a free massless scalar field φ [61]).…”

Section: Relations With Quantum Impurity Problemsmentioning

confidence: 99%

N=2 boundary supersymmetry in integrable models and perturbed boundary conformal field theory

Baseilhac¹,

Koizumi²

2003

Nuclear Physics B

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Boundary integrable models with N = 2 supersymmetry are considered. For the simplest boundary N = 2 superconformal minimal model with a Chebyshev bulk perturbation we show explicitly how fermionic boundary degrees of freedom arise naturally in the boundary perturbation in order to maintain integrability and N = 2 supersymmetry. A new boundary reflection matrix is obtained for this model and N = 2 boundary superalgebra is studied. A factorized scattering theory is proposed for a N = 2 supersymmetric extension of the boundary sine-Gordon model with either (i) fermionic or (ii) bosonic and fermionic boundary degrees of freedom. Exact results are obtained for some quantum impurity problems: the boundary scaling Lee-Yang model, a massive deformation of the anisotropic Kondo model at the filling values g = 2/(2n + 3) and the boundary Ashkin-Teller model..

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Statistics of Two-Dimensional Lattices with Four Components

Cited by 594 publications

References 1 publication

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

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

Critical interfaces of the Ashkin–Teller model at the parafermionic point

N=2 boundary supersymmetry in integrable models and perturbed boundary conformal field theory

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