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

TL;DR

This paper proves that for 2D symmetry protected topological states prepared via symmetric entanglers, the classification by the cohomology group H^3(G,U(1)) is complete, confirming a key conjecture in the field.

Contribution

The authors establish the completeness of the cohomology classification for a specific class of 2D SPT states generated by symmetric entanglers.

Findings

Classification by H^3(G,U(1)) is complete for states prepared from product states by symmetric entanglers.

Provides a rigorous proof confirming the conjecture for this class of states.

Clarifies the structure of 2D SPT phases under symmetric entangling operations.

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.