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Main Authors: Zhang, Xudong, Sun, Zhaoyu, Guo, Bin
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2511.17846
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author Zhang, Xudong
Sun, Zhaoyu
Guo, Bin
author_facet Zhang, Xudong
Sun, Zhaoyu
Guo, Bin
contents 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 $P_β$ defined on the generalized Brillouin zone restores momentum-space topology, a direct, robust real-space bulk probe has remained elusive. We resolve this by establishing a universal correspondence between $P_β$ and the entanglement polarization $χ$ of the biorthogonal ground state. Introducing a quasi-reciprocal Hamiltonian $\tilde{H}$ that removes the NHSE while preserving bulk topology, we rigorously prove the fundamental identity $P_β \equiv χ(\tilde{H})\pmod 1$ in the thermodynamic limit under the quasi-locality assumption. Crucially, we demonstrate that this equivalence transcends the locality constraints that limit traditional topological invariants. While the conventional Resta polarization fails when $\tilde{H}$ becomes non-local due to the divergence of position variance, we reveal that $χ(\tilde{H})$ 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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publishDate 2025
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spellingShingle Unified Bulk-Entanglement Correspondence in Non-Hermitian Systems
Zhang, Xudong
Sun, Zhaoyu
Guo, Bin
Quantum Physics
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 $P_β$ defined on the generalized Brillouin zone restores momentum-space topology, a direct, robust real-space bulk probe has remained elusive. We resolve this by establishing a universal correspondence between $P_β$ and the entanglement polarization $χ$ of the biorthogonal ground state. Introducing a quasi-reciprocal Hamiltonian $\tilde{H}$ that removes the NHSE while preserving bulk topology, we rigorously prove the fundamental identity $P_β \equiv χ(\tilde{H})\pmod 1$ in the thermodynamic limit under the quasi-locality assumption. Crucially, we demonstrate that this equivalence transcends the locality constraints that limit traditional topological invariants. While the conventional Resta polarization fails when $\tilde{H}$ becomes non-local due to the divergence of position variance, we reveal that $χ(\tilde{H})$ 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.
title Unified Bulk-Entanglement Correspondence in Non-Hermitian Systems
topic Quantum Physics
url https://arxiv.org/abs/2511.17846