Strange Correlators for Non-invertible Symmetry Protected Topological Phases

In this talk, we use strange correlators to differentiate between various non-invertible symmetry-protected topological (SPT) phases. Strange correlators are known to be a useful tool to distinguish ordinary invertible SPT and trivial phases. Recent studies have constructed a range of non-invertible SPT phases in various dimensions. With the non-invertible symmetry, the ordinary invertible SPTs further split into different phases. In particular, we compute the strange correlators for different non-invertible SPTs on 1+1d lattice using the matrix product states (MPS) and matrix product operators (MPO). We find that the non-invertible SPTs can be distinguished by choosing the suitable strange correlators. We demonstrate our finding by explicit calculation for the Rep(D8) SPT. We further extract the categorical data from the lattice model. In higher dimension, the structure of the non-invertible SPTs are largely unknown. The strange correlators can be used in higher dimension to distinguish between different non-invertible SPT phases and to explore the potential for discovering new quantum states.