Pseudo-Hermitian Levin-Wen models from non-semisimple TQFTs
Strongly Correlated Electrons
2022-06-07 v1 Geometric Topology
Quantum Algebra
Quantum Physics
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.
Keywords
Cite
@article{arxiv.2108.10798,
title = {Pseudo-Hermitian Levin-Wen models from non-semisimple TQFTs},
author = {Nathan Geer and Aaron D. Lauda and Bertrand Patureau-Mirand and Joshua Sussan},
journal= {arXiv preprint arXiv:2108.10798},
year = {2022}
}
Comments
21 pages, tikz diagrams, 2 figures