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Twisted Quantum Double Model of Topological Orders with Boundaries

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arxiv 1706.03611 v1 pith:5ZCUGU2W submitted 2017-06-12 cond-mat.str-el hep-thmath-phmath.MPmath.QA

classification cond-mat.str-elhep-thmath-phmath.MPmath.QA
keywords modelboundariesboundarygroupbulkdatadefineddouble
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abstract

We generalize the twisted quantum double model of topological orders in two dimensions to the case with boundaries by systematically constructing the boundary Hamiltonians. Given the bulk Hamiltonian defined by a gauge group $G$ and a three-cocycle in the third cohomology group of $G$ over $U(1)$, a boundary Hamiltonian can be defined by a subgroup $K$ of $G$ and a two-cochain in the second cochain group of $K$ over $U(1)$. The consistency between the bulk and boundary Hamiltonians is dictated by what we call the Frobenius condition that constrains the two-cochain given the three-cocyle. We offer a closed-form formula computing the ground state degeneracy of the model on a cylinder in terms of the input data only, which can be naturally generalized to surfaces with more boundaries. We also explicitly write down the ground-state wavefunction of the model on a disk also in terms of the input data only.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Planar fault-tolerant circuits for non-Clifford gates on the 2D color code

    quant-ph 2025-05 conditional novelty 8.0 of 10

    The paper constructs a family of planar fault-tolerant 'twisted color circuits' that implement logical T gates and magic-state measurements on the 2D color code via a path-integral and color-cohomology framework.

  2. Symmetry-Enriched Topological Phases and Their Gauging: A String-Net Model Realization

    cond-mat.str-el 2025-08 conditional novelty 7.0 of 10

    A string-net framework constructs exactly solvable SET lattice models from intrinsic categorical symmetries, including a nonabelian S3-enriched example whose gauging produces the S4 quantum-double phase.

  3. Handbook of Error-Correcting Codes

    quant-ph 2026-06 unverdicted novelty 2.0 of 10

    The paper compiles a curated handbook reference of error-correcting codes, their symbol-based classifications, and interrelations with mathematical objects and physical phases.

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