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arXiv · 2603.09959

A complete classification of 2d symmetry protected states with symmetric entanglers

Alex Bols·Wojciech De Roeck·Michiel De Wilde·Bruno de O. Carvalho
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Abstract

We consider symmetry protected topological states of 2d quantum spin systems, with a finite symmetry group $G$. It has been conjectured that such states are classified by the cohomology group $H^3(G,U(1))$, but the completeness of this classfication is an open problem. We restrict ourselves to symmetry protected topological states that can be prepared from a product state by a symmetric entangler. For this class of states, we prove that the classification by $H^3(G,U(1))$ is complete.

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Alex Bols, Wojciech De Roeck, Michiel De Wilde, Bruno de O. Carvalho. 2026-03-10. A complete classification of 2d symmetry protected states with symmetric entanglers. https://arxiv.org/abs/2603.09959

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