Entanglement Holography in Quantum Phases via Twisted R\'enyi-N Correlators

TL;DR

This paper develops a holographic approach to understanding entanglement in symmetry-protected topological phases, linking bulk correlators to reduced density matrices and extending the framework to thermal and mixed states.

Contribution

It introduces a novel holographic framework connecting bulk strange correlators with twisted Re9nyi-N operators in SPT phases, and generalizes this to thermal and mixed states.

Findings

Reconstruction of fixed-point SPT wavefunctions from replicated density matrices

Universal long-range order in reduced density matrices of SPT phases

Extension of twisted Re9nyi-N correlators to thermal and open quantum systems

Abstract

We introduce a holographic framework for the entanglement Hamiltonian in symmetry-protected topological (SPT) phases with area-law entanglement, whose reduced density matrix $\rho \propto e^{-H_e}$ can be treated as a lower-dimensional mixed state. By replicating $\rho$, 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 R\'enyi-N operator of the d-dimensional reduced density matrix. Notably, the reduced density matrix exhibits long-range or quasi-long-range order along the replica direction, revealing a universal entanglement feature in SPT phases. As a colloary, we generalized the framework of twisted R\'enyi-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 R\'enyi-N correlators of the surgery operator -- to characterize the topology of mixed states.