Asymptotically exact solution of the non-Hermitian disordered interacting Hatano-Nelson chain
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912595203588096 |
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| author | Mattiello, Valéria M. Quito, Victor L. Miranda, Eduardo |
| author_facet | Mattiello, Valéria M. Quito, Victor L. Miranda, Eduardo |
| contents | 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 which, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16309 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotically exact solution of the non-Hermitian disordered interacting Hatano-Nelson chain Mattiello, Valéria M. Quito, Victor L. Miranda, Eduardo Strongly Correlated Electrons Disordered Systems and Neural Networks 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 which, 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. |
| title | Asymptotically exact solution of the non-Hermitian disordered interacting Hatano-Nelson chain |
| topic | Strongly Correlated Electrons Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2509.16309 |