# On two-dimensional tensor network group symmetries

**Authors:** José Garre-Rubio, András Molnár  
**arXiv:** [2507.16475](https://arxiv.org/abs/2507.16475)  
**Date:** 2025-07-22  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2507.16475v1/

## Abstract

We introduce two-dimensional tensor network representations of finite groups carrying a 4-cocycle index. We characterize the associated gapped (2+1)D phases that emerge when these anomalous symmetries act on tensor network ground states. We further develop related tensor network unitaries that generate symmetric states representing (3+1)D symmetry protected topological phases. Although aspects of these constructions have been previously addressed, our contribution unifies them within a single tensor network framework and emphasizes the explicit formulation of local tensor equations encoding global consistency conditions.