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

TL;DR

This paper investigates spectral fluctuation properties of non-Hermitian spin chains, revealing a crossover from integrable to chaotic regimes that aligns with predictions from random matrix theory, specifically the Ginibre ensemble.

Contribution

It demonstrates how random fields induce a spectral crossover in non-Hermitian spin chains, connecting integrability, symmetry breaking, and random matrix theory predictions.

Findings

Spectral crossover from Poisson to GinUE statistics observed.

Random fields facilitate integrability and symmetry breaking.

Phenomenological models show interpolation between different Poisson regimes.

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 ($\mathcal{RT}$) 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.