2023/02/02 by Ayana Sarkar, Sarkar, Ayana, Sunidhi Sen +3
Chemistry · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Chaotic Dynamics (nlin.CD) #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Molecular spectroscopy and chirality #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2302.01423
openalex publication_date 2023/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \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 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.