Topological lattice field theories from intertwiner dynamics

Abstract

We introduce a class of 2D lattice models that describe the dynamics of intertwiners, or, in a condensed matter interpretation, the fusion and splitting of anyons. We identify different families and instances of triangulation invariant, that is, topological, models inside this class. These models give examples for symmetry protected topologically ordered 1D quantum phases with quantum group symmetries. Furthermore the models provide realizations for anyon condensation into a new effective vacuum. We explain the relevance of our findings for the problem of identifying the continuum limit of spin foam and spin net models.

35+9 pages

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• Quantum group spin nets: refinement limit and relation to spin foams
• Pachner moves in a 4d Riemannian holomorphic Spin Foam model
• Duality between Spin networks and the 2D Ising model
• Coupled intertwiner dynamics: A toy model for coupling matter to spin foam models
• BTZ Black Hole Entropy and the Turaev-Viro model
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