Entanglement holography in quantum phases via twisted Rényi- N correlators

Abstract We introduce a holographic framework for the entanglement Hamiltonian in symmetry-protected topological (SPT) phases with area-law entanglement, whose reduced density matrix (RDM) ρ ∝ e − H e 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 ( d + 1 ) -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.