Entanglement holography in quantum phases via twisted Rényi-N correlators

We introduce a holographic framework for the entanglement Hamiltonian in symmetry-protected topological (SPT) phases with area-law entanglement, whose reduced density matrix (RDM) (Formula presented) (Formula presented) can be treated as a lower-dimensional mixed state. By replicating ρ, we reconstruct the fixed-point SPT wavefunction, establishing an exact correspondence between the bulk strange correlator of the (Formula presented) (Formula presented) -dimensional SPT state and the twisted Rényi-N operator of the d-dimensional RDM. Notably, the RDM exhibits long-range or quasi-long-range order along the replica direction, revealing a universal entanglement feature in SPT phases. As a corollary, we generalized the framework of twisted Rényi-N correlator to thermal states and open quantum systems, providing an alternative formulation of the Lieb–Schultz–Mattis theorem, applicable to both closed and open systems. Finally, we extend our protocol to mixed-state SPT phases and introduce new quantum information metrics—twisted Rényi-N correlators of the surgery operator—to characterize the topology of mixed states.