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

Communications in Mathematical Physics volume 355, pages 645–689 (2017)Cite this article

A Correction to this article was published on 16 April 2018

This article has been updated

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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