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Microscopic description of 2d topological phases, duality and 3d state sums
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Doubled topological phases introduced by Kitaev, Levin and Wen supported on two dimensional lattices are Hamiltonian versions of three dimensional topological quantum field theories described by the Turaev-Viro state sum models. We introduce the latter with an emphasis on obtaining them from theories in the continuum. Equivalence of the previous models in the ground state are shown in case of the honeycomb lattice and the gauge group being a finite group by means of the well-known duality transformation between the group algebra and the spin network basis of lattice gauge theory. An analysis of the ribbon operators describing excitations in both types of models and the three dimensional geometrical interpretation are given.
Forward citations
Cited by 2 Pith papers
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From Multipartite Entanglement to TQFT
Genuine multipartite entanglement of a gapped ground state is conjectured and, for Levin-Wen models, shown to reproduce the TQFT partition function on any 3-manifold.
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ASEP/DSSYK duality and strange correlator
Moments of the DSSYK transfer matrix equal an ASEP stationary-product state overlap, presented as analogous to the strange correlator in topological state-sum models.
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