Role of phonons in the quantum chaos of Rydberg excitons

We investigate the transition from regular behavior towards chaos for Rydberg excitons in the presence of an external magnetic field. To this end, we develop a measure for chaos that is robust with respect to fluctuations in the density of states. We find that irrespective of whether or not the magnetic field is oriented along a high-symmetry direction of the crystal, all antiunitary symmetries of the system are broken for large field strengths. This result emphasizes the influence of phonons on the symmetry of Rydberg excitons. In addition, we find that the appearance of Landau levels above the band gap results in modified level spacing statistics that resemble systems without broken symmetry.