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

Abstract

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 (RT ) symmetry that has been explored analytically by Zhang and Song in [Phys.Rev.A 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 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 × 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.