# The Low-Energy TQFT of the Generalized Double Semion Model

@article{Debray2018TheLT,
title={The Low-Energy TQFT of the Generalized Double Semion Model},
author={Arun Debray},
journal={Communications in Mathematical Physics},
year={2018},
volume={375},
pages={1079-1115}
}
• A. Debray
• Published 8 November 2018
• Mathematics
• Communications in Mathematical Physics
The generalized double semion (GDS) model, introduced by Freedman and Hastings, is a lattice system similar to the toric code, with a gapped Hamiltonian whose definition depends on a triangulation of the ambient manifold M , but whose space of ground states does not depend on the triangulation, but only on the underlying manifold. In this paper, we use topological quantum field theory (TQFT) to investigate the low-energy limit of the GDS model. We define and study a functorial TQFT $$Z_{\mathrm… 6 Citations • Mathematics Communications in Mathematical Physics • 2020 We analyze the class of Generalized Double Semion (GDS) models in arbitrary dimensions from the point of view of lattice Hamiltonians. We show that on a d-dimensional spatial manifold M the dual of • Mathematics, Physics Physical Review B • 2020 We construct an exactly solvable commuting projector model for a (4+1)-dimensional {\mathbb{Z}}_{2}-symmetry-protected topological phase (SPT) which is outside the cohomology classification of • Mathematics Journal of High Energy Physics • 2021 For symmorphic crystalline interacting gapped systems we derive a classification under adiabatic evolution. This classification is complete for non-degenerate ground states. For the degenerate case • Mathematics • 2022 We introduce a framework for internal topological symmetries in quantum field theory, including “noninvertible symmetries” and “categorical symmetries”. This leads to a calculus of topological • Mathematics Geometry &amp; Topology • 2022 Author(s): Freed, Daniel S; Teleman, Constantin | Abstract: We relate two classical dualities in low-dimensional quantum field theory: Kramers-Wannier duality of the Ising and related lattice models • Mathematics • 2021 In this paper, we derive the explicit formula for higher cup products on hypercubic lattices, based on the recently developed geometrical interpretation on the simplicial complexes. We illustrate how ## References SHOWING 1-10 OF 65 REFERENCES • Mathematics • 2015 We present a generalization of the double semion topological quantum field theory to higher dimensions, as a theory of$${d-1}d-1 dimensional surfaces in a d dimensional ambient space. We construct
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