Introduces pro-tensor networks as a categorified graphical framework for many-many-body theories, recovers the Levin-Wen model, characterizes particles as modules over promonads, and relaxes semisimplicity, finiteness, and rigidity assumptions.
Jones,Dhr bimodules of quasi-local algebras and symmetric quantum cellular automata, 2304.00068
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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.
Gauging and duality transformations are equivalent up to constant depth quantum circuits in one-dimensional quantum lattice models, demonstrated via matrix product operators.
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Pro-Tensor Network
Introduces pro-tensor networks as a categorified graphical framework for many-many-body theories, recovers the Levin-Wen model, characterizes particles as modules over promonads, and relaxes semisimplicity, finiteness, and rigidity assumptions.
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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.
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From gauging to duality in one-dimensional quantum lattice models
Gauging and duality transformations are equivalent up to constant depth quantum circuits in one-dimensional quantum lattice models, demonstrated via matrix product operators.