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

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A Correction to this article was published on 16 April 2018

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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.

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Change history

  • 16 April 2018

    There were two errors in the original publication. First, the term BK in Eq. (2.20) was not well-defined in the case of non-normal subgroups K.

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Authors and Affiliations

  1. Department of Computer Science, University of California, Los Angeles, CA, 90095, USA

    Iris Cong

  2. Department of Physics, Yale University, New Haven, CT, 06520-8120, USA

    Meng Cheng

  3. Department of Mathematics, University of California, Santa Barbara, CA, 93106-6105, USA

    Zhenghan Wang

  4. Microsoft Station Q, University of California, Santa Barbara, CA, 93106-6105, USA

    Iris Cong, Meng Cheng & Zhenghan Wang

Authors
  1. Iris Cong
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  2. Meng Cheng
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  3. Zhenghan Wang
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Correspondence to Zhenghan Wang.

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Communicated by Y. Kawahigashi

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Cong, I., Cheng, M. & Wang, Z. Hamiltonian and Algebraic Theories of Gapped Boundaries in Topological Phases of Matter. Commun. Math. Phys. 355, 645–689 (2017). https://doi.org/10.1007/s00220-017-2960-4

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