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arXiv · 2607.25256

Anomalous entanglement scaling from eigenvector nonorthogonality in critical non-Hermitian free fermions

Zhenyu Xiao·Shinsei Ryu
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Abstract

Entanglement carries universal content that labels phases and critical points. We study the entanglement entropy of the steady states of critical non-Hermitian free-fermion chains. It scales logarithmically with subsystem size, but the coefficients vary continuously with the parameters and form a R\'enyi family that no single central charge can reproduce. We trace this anomaly to an ``imaginary'' Dirac point, a crossing in the imaginary part of the energy where the occupied state switches between two Bloch states. Their nonorthogonality weakens the occupation discontinuity and lowers the logarithmic coefficient. A low-energy expansion yields closed-form coefficients in excellent agreement with lattice numerics in various one-dimensional critical steady states. Remarkably, weak real onsite disorder leaves this logarithmic scaling intact and enhances the entanglement. Our results provide a generic understanding of entanglement in critical non-Hermitian free-fermion steady states.

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Zhenyu Xiao, Shinsei Ryu. 2026-07-28. Anomalous entanglement scaling from eigenvector nonorthogonality in critical non-Hermitian free fermions. https://arxiv.org/abs/2607.25256

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