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

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Hauptverfasser: Mattiello, Valéria M., Quito, Victor L., Miranda, Eduardo
Format: Preprint
Veröffentlicht: 2025
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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