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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.06206 |
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| _version_ | 1866911146662952960 |
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| author | Naichuk, Eduard Eremin, Ilya M. Brink, Jeroen van den Nogueira, Flavio S. |
| author_facet | Naichuk, Eduard Eremin, Ilya M. Brink, Jeroen van den Nogueira, Flavio S. |
| contents | The one-dimensional Hatano-Nelson model with non-reciprocal 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 non-reciprocal 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 $\mathcal{PT}$-symmetric, which leads to the existence of two regions: a region of unbroken $\mathcal{PT}$ symmetry (real-valued spectrum) and a region of broken $\mathcal{PT}$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06206 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Antiferromagnetism and spin excitations in a two-dimensional non-Hermitian Hatano-Nelson flux model Naichuk, Eduard Eremin, Ilya M. Brink, Jeroen van den Nogueira, Flavio S. Strongly Correlated Electrons The one-dimensional Hatano-Nelson model with non-reciprocal 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 non-reciprocal 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 $\mathcal{PT}$-symmetric, which leads to the existence of two regions: a region of unbroken $\mathcal{PT}$ symmetry (real-valued spectrum) and a region of broken $\mathcal{PT}$ 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. |
| title | Antiferromagnetism and spin excitations in a two-dimensional non-Hermitian Hatano-Nelson flux model |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2504.06206 |