Pro-Tensor Network
Gen Yue, Ansi Bai, Linqian Wu, Tian Lan
TLDR
Pro-Tensor Network is a new rigorous graphical framework that categorifies tensor networks, enabling the study of many-many-body theories without common constraints.
Key contributions
- Introduces the pro-tensor network, a rigorous graphical framework for "many-many-body theory."
- Provides a comprehensive toolbox for graphical calculations using pro-tensor networks.
- Recovers Levin-Wen model and generalizes Kitaev-Kong's particle characterization.
- Dispenses with semisimplicity, finiteness, and rigidity assumptions in many-body physics.
Why it matters
This paper introduces a more general and rigorous framework for studying complex many-body systems. By removing common constraints, it opens new avenues for exploring physics beyond current limitations, including generalized symmetry and topological holography.
Original Abstract
We introduce the pro-tensor network, a categorification of the tensor network, as a fully rigorous yet graphically transparent framework for studying the collection of many many-body theories, which we dub many-many-body theory. We provide a comprehensive toolbox for the graphical calculations using pro-tensor networks. As applications, we recover the Levin-Wen model as a "uniform" pro-tensor network and generalize a result of Kitaev and Kong by characterizing particles as modules over promonads. One can also interpret the string-net pro-tensor network as the space of symmetric tensor networks, thus our framework also applies to the study of generalized symmetry and topological holography. Notably, our generalization dispenses with the assumptions of semisimplicity, finiteness, and rigidity, potentially facilitating the exploration of many-body physics beyond these constraints.
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