Twisted gauge theory model of topological phases in three dimensions

Wan, Yidun; Wang, Juven; He, Huan

doi:10.1103/physrevb.92.045101

Cited by 78 publications

(102 citation statements)

References 61 publications

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“…G = (G, {1 G }, ∂ : 1 G → 1 G , id). Under this assumption, the model (2.12) reduces to a gauge model, namely the Hamiltonian realization of Dijkgraaf-Witten theory with trivial cohomology class in H 4 (BG, U(1)) [50,51]. The authors showed in [43,45] that in this case the tube algebra for loop-like excitations is isomorphic to the (untwisted) quantum triple algebra, which we reproduce below for convenience:…”

Section: Physical Interpretationmentioning

confidence: 99%

Excitations in strict 2-group higher gauge models of topological phases

Bullivant

Delcamp

2020

J. High Energ. Phys.

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We consider an exactly solvable model for topological phases in (3+1)d whose input data is a strict 2-group. This model, which has a higher gauge theory interpretation, provides a lattice Hamiltonian realisation of the Yetter homotopy 2-type topological quantum field theory. The Hamiltonian yields bulk flux and charge composite excitations that are either point-like or loop-like. Applying a generalised tube algebra approach, we reveal the algebraic structure underlying these excitations and derive the irreducible modules of this algebra, which in turn classify the elementary excitations of the model. As a further application of the tube algebra approach, we demonstrate that the ground state subspace of the three-torus is described by the central subalgebra of the tube algebra for torus boundary, demonstrating the ground state degeneracy is given by the number of elementary loop-like excitations.arXiv:1909.07937v1 [cond-mat.str-el]

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Section: Physical Interpretationmentioning

confidence: 99%

Excitations in strict 2-group higher gauge models of topological phases

Bullivant

Delcamp

2020

J. High Energ. Phys.

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“…In this case, the theory reduces to the Dijkgraaf-Witten (DW) topological gauge theory [51], whose loop braiding statistics has been thoroughly studied [2,3,52].…”

Section: A Twisted Crane-yetter Tqftmentioning

confidence: 99%

Loop Braiding Statistics and Interacting Fermionic Symmetry-Protected Topological Phases in Three Dimensions

2018

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We study Abelian braiding statistics of loop excitations in three-dimensional gauge theories with fermionic particles and the closely related problem of classifying 3D fermionic symmetry-protected topological (FSPT) phases with unitary symmetries. It is known that the two problems are related by turning FSPT phases into gauge theories through gauging the global symmetry of the former. We show that there exist certain types of Abelian loop braiding statistics that are allowed only in the presence of fermionic particles, which correspond to 3D "intrinsic" FSPT phases, i.e., those that do not stem from bosonic SPT phases. While such intrinsic FSPT phases are ubiquitous in 2D systems and in 3D systems with antiunitary symmetries, their existence in 3D systems with unitary symmetries was not confirmed previously due to the fact that strong interaction is necessary to realize them. We show that the simplest unitary symmetry to support 3D intrinsic FSPT phases is Z 2 × Z 4 . To establish the results, we first derive a complete set of physical constraints on Abelian loop braiding statistics. Solving the constraints, we obtain all possible Abelian loop braiding statistics in 3D gauge theories, including those that correspond to intrinsic FSPT phases. Then, we construct exactly soluble state-sum models to realize the loop braiding statistics. These state-sum models generalize the well-known Crane-Yetter and Dijkgraaf-Witten models.

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“…One is how to develop a similar approach to solve discrete (3+1)-dimensional models [33][34][35] for topological phases. The observable algebra [of local operators that commute with the Hamiltonian, which is the tube algebra in (2+1)-dimensional case] will be expanded due to the extra dimension.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Full dyon excitation spectrum in extended Levin-Wen models

Geer

2018

Phys. Rev. B

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In Levin-Wen (LW) models, a wide class of exactly solvable discrete models, for two-dimensional topological phases, it is relatively easy to describe only single-fluxon excitations, but not the charge and dyonic as well as many-fluxon excitations. To incorporate charged and dyonic excitations in (doubled) topological phases, an extension of the LW models is proposed in this paper. We first enlarge the Hilbert space with adding a tail on one of the edges of each trivalent vertex to describe the internal charge degrees of freedom at the vertex. Then, we study the full dyon spectrum of the extended LW models, including both quantum numbers and wave functions for dyonic quasiparticle excitations. The local operators associated with the dyonic excitations are shown to form the so-called tube algebra, whose representations (modules) form the quantum double (categoric center) of the input data (unitary fusion category). In physically relevant cases, the input data are from a finite or quantum group (with braiding R matrices), and we find that the elementary excitations (or dyon species), as well as any localized/isolated excited states, are characterized by three quantum numbers: charge, fluxon type, and twist. They provide a "complete basis" for many-body states in the enlarged Hilbert space. Concrete examples are presented and the relevance of our results to the electric-magnetic duality existing in the models is addressed.

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Twisted gauge theory model of topological phases in three dimensions

Cited by 78 publications

References 61 publications

Excitations in strict 2-group higher gauge models of topological phases

Excitations in strict 2-group higher gauge models of topological phases

Loop Braiding Statistics and Interacting Fermionic Symmetry-Protected Topological Phases in Three Dimensions

Full dyon excitation spectrum in extended Levin-Wen models

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