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

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.