# GOE-GUE-Poisson transitions in the nearest neighbor spacing distribution of magnetoexcitons

## TL;DR

This paper studies how the statistical distribution of energy level spacings in magnetoexcitons transitions between Poisson, GOE, and GUE types under varying magnetic field angles and energies, confirming theoretical predictions.

## Contribution

It demonstrates the transitions between different random matrix theory statistics in magnetoexcitons, validating analytical formulas and the Wigner surmise in this system.

## Key findings

- Transitions between GOE and GUE observed with magnetic field angle changes.
- Transitions between Poissonian and GUE statistics confirmed.
- Good agreement with random matrix theory predictions.

## Abstract

Recent investigations on the Hamiltonian of excitons by F. Schweiner et al. [Phys. Rev. Lett. 118, 046401 (2017)] revealed that the combined presence of a cubic band structure and external fields breaks all antiunitary symmetries. The nearest neighbor spacing distribution of magnetoexcitons can exhibit Poissonian statistics, the statistics of a Gaussian orthogonal ensemble (GOE) or a Gaussian unitary ensemble (GUE) depending on the system parameters. Hence, magnetoexcitons are an ideal system to investigate the transitions between these statistics. Here we investigate the transitions between GOE and GUE statistics and between Poissonian and GUE statistics by changing the angle of the magnetic field with respect to the crystal lattice and by changing the scaled energy known from the hydrogen atom in external fields. Comparing our results with analytical formulae for these transitions derived with random matrix theory, we obtain a very good agreement and thus confirm the Wigner surmise for the exciton system.