# Disentangling the Generalized Double Semion Model

## TL;DR

This paper studies the structure of Generalized Double Semion models in various dimensions, revealing their relation to cohomology theories and their behavior under time reversal symmetry, with implications for topological quantum field theories.

## Contribution

It demonstrates that GDS models are equivalent to cohomology theories up to local quantum circuits and explores their symmetry properties in odd dimensions.

## Key findings

- GDS duals relate to group cohomology and lower-dimensional models.
- GDS models form non-trivial symmetry enriched phases with time reversal.
- Results have implications for topological quantum field theories.

## Abstract

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 the GDS is equivalent, up to constant depth local quantum circuits, to a group cohomology theory tensored with lower dimensional cohomology models that depend on the manifold $M$. We comment on the space-time topological quantum field theory (TQFT) interpretation of this result. We also investigate the GDS in the presence of time reversal symmetry, showing that it forms a non-trivial symmetry enriched toric code phase in odd spatial dimensions.