Spectral crossovers and universality in quantum spin chains coupled to random fields

We study the spectral properties of and crossovers between different random matrix ensembles [Poissonian, Gaussian orthogonal ensemble (GOE), unitary (GUE)] in correlated spin-chain systems, presence magnetic fields, scalar spin-chirality term, competing with usual isotropic time-reversal invariant Heisenberg term. have investigated these context level-spacing distribution ratio distribution. use theory (RMT) analytical results to fit observed Poissonian-to-GOE GOE-to-GUE crossovers, examine relationship RMT crossover parameter $\ensuremath{\lambda}$ scaled physical parameters systems terms a scaling exponent. find that behavior exhibits universality, sense that, it becomes independent lattice size large Hamiltonian dimension limit. Moreover, exponent obtained from such finite analysis, seems be quite robust type considered or specific correlation measure used.