Pseudo-Hermitian Levin-Wen models from non-semisimple TQFTs
arXiv:2108.10798 · doi:10.1016/j.aop.2022.168937
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.
21 pages, tikz diagrams, 2 figures
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Cited by in corpus (4)
- Universal quantum computation using Ising anyons from a non-semisimple Topological Quantum Field Theory
- A Hermitian TQFT from a non-semisimple category of quantum sl(2)-modules
- Non-semisimple Levin-Wen Models and Hermitian TQFTs from quantum (super)groups
- Density and unitarity of the Burau representation from a non-semisimple TQFT