Entanglement Holography in Quantum Phases via Twisted Rényi-N Correlators

• URL: http://arxiv.org/abs/2506.10076v1
• Date: Wed, 11 Jun 2025 18:00:22 GMT
• Title: Entanglement Holography in Quantum Phases via Twisted Rényi-N Correlators
• Authors: Pablo Sala, Frank Pollmann, Masaki Oshikawa, Yizhi You,
• Abstract summary: We introduce a holographic framework for the entanglement Hamiltonian in symmetry-protected topological phases with area-law entanglement.<n>We show that the reduced density matrix $rho propto e-H_e$ can be treated as a lower-dimensional mixed state.<n>As a colloary, we generalized the framework of twisted R'enyi-N correlator to thermal states and open quantum systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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