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  • Letter

Unified topological bulk-entanglement correspondence for the polarization in non-Hermitian systems

Xudong Zhang1, Zhaoyu Sun2, and Bin Guo1,*

  • *Contact author: binguo@whut.edu.cn

Phys. Rev. B 113, L100401 – Published 2 March, 2026

DOI: https://doi.org/10.1103/4pnb-mqmr

Abstract

The non-Hermitian skin effect (NHSE) fundamentally invalidates the conventional bulk-boundary correspondence (BBC), leading topological diagnostics into a crisis. While the non-Bloch polarization Pβ, defined on the generalized Brillouin zone, successfully captures momentum-space topology, a purely real-space characterization of non-Bloch topology has remained unclear. In this work, we establish a correspondence between Pβ and the entanglement polarization χ of the biorthogonal ground state, understood as a geometric and entanglement-based indicator rather than a physical electric polarization. By introducing a quasireciprocal Hamiltonian H̃, which removes the NHSE while preserving bulk spectrum and topology, we rigorously prove the fundamental identity Pβ≡χ(H̃)(mod1) in the thermodynamic limit under the quasilocality assumption. Crucially, we demonstrate that this equivalence transcends the locality constraints that limit traditional topological invariants. While the conventional Resta polarization fails when H̃ becomes nonlocal due to the divergence of position variance, we reveal that χ(H̃) remains robustly quantized, protected by the Fredholm index of Toeplitz operators. Our work thus identifies entanglement as the unique real-space diagnostic capable of capturing non-Bloch topology beyond the breakdown of locality, successfully restoring the BBC across diverse non-Hermitian systems such as line-gap, point-gap, and gapless phases, thereby unifying the geometric and entanglement paradigms in non-Hermitian physics.

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