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

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 Rényi 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.

Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Quantum Physics (quant-ph)

arXiv:2607.25256 [cond-mat.mes-hall]

(or arXiv:2607.25256v1 [cond-mat.mes-hall] for this version)

https://doi.org/10.48550/arXiv.2607.25256 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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