(3+1)-TQFTs and topological insulators

By Kevin Walker, Zhenghan Wang. 2011

243 citations recorded by the source corpus.

Levin-Wen models are microscopic spin models for topological phases of matter in (2+1)-dimension. We introduce a generalization of such models to (3 + 1)-dimension based on unitary braided fusion categories, also known as unitary premodular categories. We discuss the ground state degeneracy on 3-manifolds and statistics of excitations which include both points and defect loops. Potential connections with recently proposed fractional topological insulators and projective ribbon permutation statistics are described.

Subfields: Atomic and Molecular Physics, and Optics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b3bae8b888421bf1777f22b87371130593c2ce55

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In Atomic and Molecular Physics, and Optics

In Geometry and Topology

Citations in the corpus

Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect (2012, background): “This theta value implies, for example, that the domain wall between opposite time-reversal-symmetrybreaking regions on the surface induces a protected 011016-2 mode, which is the edge state corresponding to the xy ¼ 2 quantized Hall effect of bosons.”
Comments on one-form global symmetries and their gauging in 3d and 4d (2018, background): “Examples of such UV theories are a PSU(N) gauge theory (discussed in Section 4) and the Walker-Wang lattice model [18,19,46].”
Braiding Statistics and Link Invariants of Bosonic/Fermionic Topological Quantum Matter in 2+1 and 3+1 dimensions (2016, methodology): “Another possible formulation for beyond-Dijkgraaf-Witten model can be the Walker-Wang model [39, 40].”
Quantum memories at finite temperature (2014, background): “Topological quantum field theories, and extensions thereupon (Haah, 2011; Hamma et al., 2005c; Walker and Wang, 2012; Yoshida, 2013) give rise to classes of models that are of interest in the field of quantum memories.”
Higher symmetry and gapped phases of gauge theories (2013, methodology): “Indeed, it has been conjectured in [10] (see also [11]) that in the continuum limit WalkerWang models based on Zn are described by a BF action deformed by a term B ∧ B.”
Non-Abelian Topological Order on the Surface of a 3D Topological Superconductor from an Exactly Solved Model (2013, methodology): “Figure 5: Plaquette term in Walker-Wang model (taken from [29]).”
On classification of modular categories by rank (2015, background): “A classification of modular categories is literally a classification of certain topological phases of matter [32, 6].”
Long-Range Entanglement from Measuring Symmetry-Protected Topological Phases (2021, methodology): “The preparation of such a state can prove useful for measurement-based quantum computation using such Walker-Wang models[156] by effectively evolving the two-dimensional topological order on the boundary using measurements[157, 158].”
Topological phases with generalized global symmetries (2015, methodology): “Our lattice models, before and after coupling to gauge fields, presumably satisfy these consistency equations of category theoretical approaches, and are beyond known theories of topological order, such as the WalkerWang model [10] and the Dijkgraaf-Witten topological gauge theories [1].”