R-TNR builds fusion-category symmetry into Loop-TNR and recovers anyon-resolved conformal spectra, spins, and structure constants for Ising, tricritical Ising, and three-state Potts to high accuracy.
Holography for bulk-boundary local topo- logical order
5 Pith papers cite this work. Polarity classification is still indexing.
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abstract
In our previous article [arXiv:2307.12552], we introduced local topological order (LTO) axioms for quantum spin systems which allowed us to define a physical boundary (associated to a cut of the lattice) manifested by a net of boundary algebras in one dimension lower. This gives a formal setting for topological holography, where the braided tensor category of DHR bimodules of the physical boundary algebra captures the bulk topological order. In this article, we extend the LTO axioms to quantum spin systems equipped with a topological boundary (domain wall with the trivial phase), again producing a physical boundary algebra for the bulk-boundary system, whose category of (topological) boundary DHR bimodules recovers the topological boundary order. We perform this analysis in explicit detail for Levin-Wen and Walker-Wang bulk-boundary systems. Along the way, we introduce a 2D braided categorical net of algebras built from a unitary braided fusion category (UBFC). Such nets arise as boundary algebras of Walker-Wang models. We consider the canonical state on this braided categorical net corresponding to the standard topological boundary for the Walker-Wang model. Interestingly, in this state, the cone von Neumann algebras are type I with finite dimensional centers, in contrast with the type II and III cone von Neumann algebras from the Levin-Wen models studied in [arXiv:2307.12552]. The superselection sectors recover the underlying unitary category of our UBFC, and it was recently proven in [arXiv:2609.20725] that the superselection category also captures the fusion and braiding.
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Superselection sectors of nets on geometric posets get a localization-free Connes fusion tensor product and braiding, and for 2D braided categorical nets the sector category is braided-equivalent to the opposite ind-completion of the underlying unitary braided fusion category.
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.
citing papers explorer
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Algebraic Tensor Network Renormalization and Holographic duality
R-TNR builds fusion-category symmetry into Loop-TNR and recovers anyon-resolved conformal spectra, spins, and structure constants for Ising, tricritical Ising, and three-state Potts to high accuracy.
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Superselection theory for 2D braided quantum spin systems via Connes fusion
Superselection sectors of nets on geometric posets get a localization-free Connes fusion tensor product and braiding, and for 2D braided categorical nets the sector category is braided-equivalent to the opposite ind-completion of the underlying unitary braided fusion category.
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Parameterized Families of Toric Code Phase: $em$-duality family and higher-order anyon pumping
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.
- Connecting the tensor-categorical formulation of anyon condensation with operator algebras and entropic order parameters
- Universal fusion category symmetries on tensor products of infinite-dimensional Hilbert spaces