Correspondence between symmetry breaking of 2-level systems and disorder in Rosenzweig-Porter ensemble

Random Matrix Theory (RMT) provides a tool to understand physical systems in which spectral properties can be changed from Poissonian (integrable) to Wigner-Dyson (chaotic). Such transitions can be seen in Rosenzweig-Porter ensemble (RPE) by tuning the fluctuations in the random matrix elements. We show that integrable or chaotic regimes in any 2-level system can be uniquely controlled by the symmetry-breaking properties. We compute the Nearest Neighbour Spacing (NNS) distributions of these matrix ensembles and find that they exactly match with that of RPE. Our study indicates that the loss of integrability can be exactly mapped to the extent of disorder in 2-level systems.