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We systematically study the short range spectral fluctuation properties ofthree non-hermitian spin chain hamiltonians using complex spacing ratios. Inparticular we focus on the non-hermitian version of the standardone-dimensional anisotropic XY model having intrinsic rotation-time-reversal($\mathcal{RT}$) symmetry that has been explored analytically by Zhang and Songin [Phys.Rev.A {\bf 87}, 012114 (2013)]. The corresponding hermitiancounterpart is also exactly solvable and has been widely employed as a toymodel in several condensed matter physics problems. We show that the presenceof a random field along the $x$-direction together with the one along $z$facilitates integrability and $\mathcal{RT}$-symmetry breaking leading to theemergence of quantum chaotic behaviour indicated by a spectral crossoverresembling Poissonian to Ginibre unitary ensemble (GinUE) statistics of randommatrix theory. Additionally, we consider two $n \times n$ dimensionalphenomenological random matrix models in which, depending upon crossoverparameters, the fluctuation properties measured by the complex spacing ratiosshow an interpolation between 1D-Poisson to GinUE and 2D-Poisson to GinUEbehaviour. Here 1D and 2D Poisson correspond to real and complex uncorrelatedlevels, respectively.

Spectral crossover in non-hermitian spin chains: comparison with random matrix theory