Symmetry-twisted multi-entropies: Order parameters for 2D SPT phases
The paper proposes two nonlocal order parameters, symmetry-twisted multi-entropies, to detect and distinguish all bosonic SPT phases in 2D protected by internal discrete Abelian unitary symmetries. These parameters are constructed by simulating the SPT path integral on non-trivial spacetime manifolds. The results show these quantities correspond directly to topological invariants derived from TQFT on lens spaces and three-tori, proving multipartite entanglement is a defining feature of these phases.