Boundary and domain wall theories of 2d generalized quantum double model

Jia, Zhih-Ahn; Kaszlikowski, Dagomir; Sheng, T. T.

doi:10.1007/jhep07(2023)160

Cited by 7 publications

(1 citation statement)

References 74 publications

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“…From a topologically ordered phase perspective, a quantum double model is a lattice realization of the 2d non-chiral topological order [6,[15][16][17][18]. The 2d topologically ordered phase is mathematically characterized by a unitary modular tensor category (UMTC) D = (D, ⊕, ⊗, 1, α, β, θ) [19][20][21], where α, β, θ are associator, braiding, and twist.…”

Section: Introductionmentioning

confidence: 99%

Electric-magnetic duality and Z 2 symmetry enriched Abelian lattice gauge theory

Jia,

Kaszlikowski,

Tan

2024

J. Phys. A: Math. Theor.

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Kitaev's quantum double model is a lattice realization of Dijkgraaf-Witten topological quantum field theory (TQFT), its topologically protected ground state space has broad applications for topological quantum computation and topological quantum memory. We investigate the Z2 symmetry enriched generalization of the model for the Abelian group in a categorical framework and present an explicit Hamiltonian construction. This model provides a lattice realization of the Z2 symmetry of the topological phase. We discuss in detail the categorical symmetry of the phase, for which the electric-magnetic (EM) duality symmetry is a special case. The aspects of symmetry defects are investigated using the G-crossed unitary braided fusion category (UBFC). By determining the corresponding anyon condensation, the gapped boundaries and boundary-bulk duality are also investigated. In the last part, an explicit lattice realization of EM duality is discussed.

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Section: Introductionmentioning

confidence: 99%

Electric-magnetic duality and Z 2 symmetry enriched Abelian lattice gauge theory

Jia,

Kaszlikowski,

Tan

2024

J. Phys. A: Math. Theor.

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Symmetry fractionalized (irrationalized) fusion rules and two domain-wall Verlinde formulae

Zhao,

Wang,

et al. 2024

J. High Energ. Phys.

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We investigate the composite systems consisting of topological orders separated by gapped domain walls. We derive a pair of domain-wall Verlinde formulae, that elucidate the connection between the braiding of interdomain excitations labeled by pairs of anyons in different domains and quasiparticles in the gapped domain wall with their respective fusion rules. Through explicit non-Abelian examples, we showcase the calculation of such braiding and fusion, revealing that the fusion rules for interdomain excitations are generally fractional or irrational. By investigating the correspondence between composite systems and anyon condensation, we unveil the reason for designating these fusion rules as symmetry fractionalized (irrationalized) fusion rules. Our findings hold promise for applications across various fields, such as topological quantum computation, topological field theory, conformal field theory, and parton physics.

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Weak Hopf symmetry and tube algebra of the generalized multifusion string-net model

Jia,

Tan,

Kaszlikowski

2024

J. High Energ. Phys.

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We investigate the multifusion generalization of string-net ground states and lattice Hamiltonians, delving into their associated weak Hopf symmetries. For the multifusion string-net, the gauge symmetry manifests as a general weak Hopf algebra, leading to a reducible vacuum string label; the charge symmetry, serving as a quantum double of gauge symmetry, constitutes a connected weak Hopf algebra. This implies that the associated topological phase retains its characterization by a unitary modular tensor category (UMTC). The bulk charge symmetry can also be captured by a weak Hopf tube algebra. We offer an explicit construction of the weak Hopf tube algebra structure and thoroughly discuss its properties. The gapped boundary and domain wall models are extensively discussed, with these 1d phases characterized by unitary multifusion categories (UMFCs). We delve into the gauge and charge symmetries of these 1d phases, as well as the construction of the boundary and domain wall tube algebras. Additionally, we illustrate that the domain wall tube algebra can be regarded as a cross product of two boundary tube algebras. As an application of our model, we elucidate how to interpret the defective string-net as a restricted multifusion string-net.

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Boundary and domain wall theories of 2d generalized quantum double model

Cited by 7 publications

References 74 publications

Electric-magnetic duality and Z 2 symmetry enriched Abelian lattice gauge theory

Electric-magnetic duality and Z 2 symmetry enriched Abelian lattice gauge theory

Symmetry fractionalized (irrationalized) fusion rules and two domain-wall Verlinde formulae

Weak Hopf symmetry and tube algebra of the generalized multifusion string-net model

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