Universal transition of spectral fluctuation in particle–hole symmetric system

We study the spectral properties of a multiparametric system having particle-hole symmetry in random matrix setting. observe crossover from Poisson to Wigner-Dyson like behavior average local ratio spacing within spectrum single as function effective parameter referred complexity parameter. The varies logarithmically across transition. This is universal for different ensembles subjected same constraint symmetry. universality this dependence further established by studying interpolating ensemble connecting systems with that chiral For each remains logarithmic verify fluctuation case 2D Su-Schrieffer-Heeger (SSH) model along on during transition integrable non-integrable limit.