Hamiltonian and Algebraic Theories of Gapped Boundaries in Topological Phases of Matter

Abstract

We present an exactly solvable lattice Hamiltonian to realize gapped boundaries of Kitaev's quantum double models for Dijkgraaf-Witten theories. We classify the elementary excitations on the boundary, and systematically describe the bulk-to-boundary condensation procedure. We also present the parallel algebraic/categorical structure of gapped boundaries.

arXiv comment43 pages, 37 figures. Replaces Ch. 2.1-5, 2.7-8, 3.1-5, 3.7-8 of arXiv:1609.02037. Published version contained inaccuracy/redundancy in Eqs. 2.19-23 and inaccuracy in Thm. 2.12; these are corrected in this version

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