Anyon Condensation and Its Applications

Burnell, F. J.

doi:10.1146/annurev-conmatphys-033117-054154

Cited by 112 publications

(98 citation statements)

References 154 publications

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“…Based on string-net models and general principles of anyon condensation [84][85][86][87][88], we now discuss a construction of non-Abelian fracton models. Following the discussion in Sec.…”

Section: Cage-net Fracton Modelsmentioning

confidence: 99%

“…Our work goes beyond this construction by considering stringnet models whose excitations are non-Abelian anyons. Based on general principles of anyon condensation in tensor categories [84][85][86][87][88], we then establish the existence of deconfined dim-1 excitations with non-Abelian braiding statistics in the condensed d = 3 fracton phases. Some other works have discussed fracton models with non-Abelian excitations.…”

Section: Introductionmentioning

confidence: 99%

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Cage-Net Fracton Models

et al. 2019

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We introduce a class of gapped three-dimensional models, dubbed "cage-net fracton models," which host immobile fracton excitations in addition to non-Abelian particles with restricted mobility. Starting from layers of two-dimensional string-net models, whose spectrum includes non-Abelian anyons, we condense extended one-dimensional "flux-strings" built out of point-like excitations. Flux-string condensation generalizes the concept of anyon condensation familiar from conventional topological order and allows us to establish properties of the fracton ordered (equivalently, flux-string condensed) phase, such as its ground state wave function and spectrum of excitations. Through the examples of doubled Ising and SU(2) k cage-net models, we demonstrate the existence of strictly immobile Abelian fractons and of non-Abelian particles restricted to move only along one dimension. In the doubled Ising cage-net model, we show that these restricted-mobility non-Abelian excitations are a fundamentally three-dimensional phenomenon, as they cannot be understood as bound states amongst two-dimensional non-Abelian anyons and Abelian particles. We further show that the ground state wave function of such phases can be understood as a fluctuating network of extended objects -cages -and strings, which we dub a cage-net condensate. Besides having implications for topological quantum computation in three dimensions, our work may also point the way towards more general insights into quantum phases of matter with fracton order.

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“…Based on string-net models and general principles of anyon condensation [84][85][86][87][88], we now discuss a construction of non-Abelian fracton models. Following the discussion in Sec.…”

Section: Cage-net Fracton Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Cage-Net Fracton Models

et al. 2019

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“…In this work, we make a first step to resolve this issue, focusing on quantum phase transitions between different gapped SETOs driven by anyon condensation [BS09, Kon14, NHvK + 16, NHK + 16, Bur18]. We develop a categorical framework for spontaneous symmetry breaking driven by condensing anyons in topological orders.…”

Section: Introductionmentioning

confidence: 99%

Spontaneous symmetry breaking from anyon condensation

Bischoff

Jones

Lü

et al. 2019

J. High Energ. Phys.

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In a physical system undergoing a continuous quantum phase transition, spontaneous symmetry breaking occurs when certain symmetries of the Hamiltonian fail to be preserved in the ground state. In the traditional Landau theory, a symmetry group can break down to any subgroup. However, this no longer holds across a continuous phase transition driven by anyon condensation in symmetry enriched topological orders (SETOs). For a SETO described by a Gcrossed braided extension C ⊆ C × G , we show that physical considerations require that a connected etale algebra A ∈ C admit a G-equivariant algebra structure for symmetry to be preserved under condensation of A. Given any categorical action G → Aut br ⊗ (C) such that g(A) ∼ = A for all g ∈ G, we show there is a short exact sequence whose splittings correspond to G-equivariant algebra structures. The non-splitting of this sequence forces spontaneous symmetry breaking under condensation of A. Furthermore, we show that if symmetry is preserved, there is a canonically associated SETO of C loc A , and gauging this symmetry commutes with anyon condensation.

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“…There is another process, that leads to phases for such SU(2) k systems as considered here, known as anyon condensation [112][113][114]. The transitions between k andk are however (generically) different from anyon condensation.…”

Section: √λmentioning

confidence: 95%

Cosmological Constant from Condensation of Defect Excitations

Dittrich

2018

Universe

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A key challenge for many quantum gravity approaches is to construct states that describe smooth geometries on large scales. Here we define a family of (2 + 1)-dimensional quantum gravity states which arise from curvature excitations concentrated at point like defects and describe homogeneously curved geometries on large scales. These states represent therefore vacua for three-dimensional gravity with different values of the cosmological constant. They can be described by an anomaly-free first class constraint algebra quantized on one and the same Hilbert space for different values of the cosmological constant. A similar construction is possible in four dimensions, in this case the curvature is concentrated along string-like defects and the states are vacua of the Crane-Yetter model. We will sketch applications for quantum cosmology and condensed matter.

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Anyon Condensation and Its Applications

Cited by 112 publications

References 154 publications

Cage-Net Fracton Models

Cage-Net Fracton Models

Spontaneous symmetry breaking from anyon condensation

Cosmological Constant from Condensation of Defect Excitations

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