Unified Bulk-Entanglement Correspondence in Non-Hermitian Systems

• URL: http://arxiv.org/abs/2511.17846v1
• Date: Sat, 22 Nov 2025 00:13:11 GMT
• Title: Unified Bulk-Entanglement Correspondence in Non-Hermitian Systems
• Authors: Xudong Zhang, Zhaoyu Sun, Bin Guo,
• Abstract summary: We prove the fundamental identity $P_ equiv (tildeH)pmod 1$ in the thermodynamic limit under the quasi-locality assumption.<n>While the conventional Resta polarization fails when $tildeH$ becomes non-local due to the divergence of position variance, we reveal that $(tildeH)$ remains robustly quantized.
• Score: 5.694212399220084
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $P_β$ 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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