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

• URL: http://arxiv.org/abs/2108.10798v1
• Date: Tue, 24 Aug 2021 15:39:41 GMT
• Title: Pseudo-Hermitian Levin-Wen models from non-semisimple TQFTs
• Authors: Nathan Geer, Aaron D. Lauda, Bertrand Patureau-Mirand, Joshua Sussan
• Abstract summary: We construct large classes of exactly solvable pseudo-Hermitian 2D spin Hamiltonians. 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.
• Score: 24.70079638524539
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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