Communications in Mathematical Physics

, Volume 355, Issue 2, pp 645–689 | Cite as

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

  • Iris Cong
  • Meng Cheng
  • Zhenghan WangEmail author


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.


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© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of CaliforniaLos AngelesUSA
  2. 2.Department of PhysicsYale UniversityNew HavenUSA
  3. 3.Department of MathematicsUniversity of CaliforniaSanta BarbaraUSA
  4. 4.Microsoft Station QUniversity of CaliforniaSanta BarbaraUSA

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