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Antiferromagnetism and spin excitations in a two-dimensional non-Hermitian Hatano-Nelson flux model

Eduard Naichuk1,2, Ilya M. Eremin3, Jeroen van den Brink1,4, and Flavio S. Nogueira1

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Phys. Rev. B 112, 115120 – Published 9 September, 2025

DOI: https://doi.org/10.1103/1j93-nk3x

Abstract

The one-dimensional Hatano-Nelson model with nonreciprocal hoppings is a prominent example of a relatively simple non-Hermitian quantum-mechanical system, which allows to study various phenomena in open quantum systems without adding extra gain and loss terms. Here we propose to use it as a building block to construct a correlated non-Hermitian Hamiltonian in two dimensions. It has the characteristic form of a flux model with clock-anticlockwise nonreciprocal hopping on each plaquette. Adding the on-site Hubbard type interaction, we analyze the formation of the longe-range antiferromagnetic order and its spin excitations. Such a model is non-Hermitian, but PT-symmetric, which leads to the existence of two regions: a region of unbroken PT symmetry (real-valued spectrum) and a region of broken PT symmetry with exceptional lines and complex-valued energy spectrum. The transition from one region to another is controlled by the value of the on-site interaction parameter and coincides with the metal-insulator transition. We also analyze the spin wave spectrum, which is characterized by two diffusive d-wave type of modes corresponding to gain and loss.

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Phys. Rev. B 112, 115120– Published 9 September, 2025
  • Received 10 April 2025
  • Revised 22 August 2025
  • Accepted 26 August 2025
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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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