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arXiv · 2108.10798

Pseudo-Hermitian Levin-Wen models from non-semisimple TQFTs

Nathan Geer·Aaron D. Lauda·Bertrand Patureau-Mirand·Joshua Sussan
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Abstract

We construct large classes of exactly solvable pseudo-Hermitian 2D spin Hamiltonians. The ground states of these systems depend only on the spatial topology of the system. We identify the ground state system on a surface with the value assigned to the surface by a non-semisimple TQFT generalizing the Turaev-Viro model. A non-trivial example arises from a non-semisimple subcategory of representations of quantum sl(2) where the quantum parameter is specialized to a root of unity.

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Nathan Geer, Aaron D. Lauda, Bertrand Patureau-Mirand, Joshua Sussan. 2021-08-24. Pseudo-Hermitian Levin-Wen models from non-semisimple TQFTs. https://doi.org/10.1016/j.aop.2022.168937

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