Anomalous critical scaling of biorthogonal entanglement in the non-Hermitian topological Anderson insulator

Hatay Mustafa Kemal University, Department of Physics - Antakya, Hatay, Turkey

Received: 12 December 2025
Accepted: 17 March 2026

Abstract

The characterization of topological phases in disordered non-Hermitian systems remains a formidable challenge, as the non-Hermitian skin effect (NHSE) disrupts the conventional bulk-boundary correspondence and renders spectral invariants unreliable. In this letter, we propose the real part of the biorthogonal entanglement entropy as a precise, basis-independent diagnostic that cuts through this complexity. Investigating a disordered non-reciprocal Kitaev chain, we demonstrate that this entropic probe provides a robust, boundary-sensitive diagnostic that faithfully tracks the topological phase transition even in regimes where traditional winding numbers fluctuate wildly. Crucially, we uncover an anomalous critical scaling of the entanglement entropy: while the Hermitian limit follows standard conformal scaling , the non-Hermitian critical point exhibits a super-critical effective central charge of . Within the studied system sizes , this enhancement is consistent with skin-effect–driven non-unitary behavior at the critical point. Our findings establish biorthogonal entanglement not only as a robust order parameter for the topological Anderson insulator but also as an experimentally accessible signature in topo-electric circuits.