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  • Letter
  • Open Access

Asymptotically exact solution of the non-Hermitian disordered interacting Hatano-Nelson chain

Valéria M. Mattiello1, Victor L. Quito2,*, and Eduardo Miranda1

  • *Contact author: vquito@ifsc.usp.br
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Phys. Rev. Research 8, L032012 – Published 22 July, 2026

DOI: https://doi.org/10.1103/jbb1-gcbh

Abstract

We present an asymptotically exact solution of a paradigmatic non-Hermitian model: the disordered interacting fermionic Hatano-Nelson model, or equivalently, the non-Hermitian spin-1/2 XXZ model. We use a renormalization group method suited for disordered systems and show that non-Hermitian couplings are relevant perturbations to the Hermitian model, which ultimately leads to a quantum-to-classical crossover. The ground state of the model consists of a collection of strongly coupled pairs of spins of arbitrary size at random positions that, unlike the Hermitian case, do not form singlets, but a mixture of the singlet and the M=0 triplet state. As a result, the magnetic susceptibility in the x−y directions becomes negative and diverges at a finite small temperature. Additionally, in sharp contrast to the ln(L) increase observed in disordered Hermitian chains, the entanglement entropy of a partition of size L saturates for large L, as the strongly coupled pairs become classical and stop contributing at large length scales.

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Phys. Rev. Research 8, L032012– Published 22 July, 2026
  • Received 24 September 2025
  • Accepted 9 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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