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Duality via Sequential Quantum Circuit in the Topological Holography Formalism

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arxiv 2409.06647 v2 pith:YBXFUZ4R submitted 2024-09-10 cond-mat.str-el quant-ph

Robijn Vanhove , Vibhu Ravindran , David T. Stephen , Xiao-Gang Wen , Xie Chen This is my paper
classification cond-mat.str-elquant-ph
keywords boundarydualitytopologicalformalismholographyquantumcircuitcorresponding
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Two quantum theories which look different but are secretly describing the same low-energy physics are said to be dual to each other. When realized in the Topological Holography formalism, duality corresponds to changing the gapped boundary condition on the top boundary of a topological field theory, which determines the symmetry of the system, while not affecting the bottom boundary where all the dynamics take place. In this paper, we show that duality in the Topological Holography formalism can be realized with a Sequential Quantum Circuit applied to the top boundary. As a consequence, the Hamiltonians before and after the duality mapping have exactly the same spectrum in the corresponding symmetry sectors, and the entanglement in the corresponding low-energy eigenstates differs by at most an area law term.

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Cited by 3 Pith papers

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

  1. Fracton Topological Holography

    quant-ph 2026-06 unverdicted novelty 7.0 of 10

    Introduces FTH as an extension of TH/SymTFT to type-I and type-II fracton orders, demonstrating boundary switches and dualities for X-cube and Haah's code via stabilizer formalism.

  2. Parameterized Families of Toric Code Phase: $em$-duality family and higher-order anyon pumping

    cond-mat.str-el 2026-05 unverdicted novelty 7.0 of 10

    Parameterized families of toric code Hamiltonians realize em-duality pumping and higher-order anyon pumping, diagnosed by topological pumping into tensor-network bond spaces and corner modes.

  3. ASEP/DSSYK duality and strange correlator

    hep-th 2026-06 unverdicted novelty 5.0 of 10

    Moments of the DSSYK transfer matrix equal an ASEP stationary-product state overlap, presented as analogous to the strange correlator in topological state-sum models.

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