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

Quantum Physics;Disordered Systems and Neural Networks;Chaotic Dynamics