RMT Spectral Distribution Crossovers in Random Spin Chains

We study spectral properties and spectral-crossovers between different random matrix ensembles (Poissonian, GOE, GUE) in correlated spin chain systems, in the presence of random magnetic fields, and scalar spin-chirality term, as a function of competing Hamiltonian parameters. We have investigated these crossovers in the context of level-spacing distribution and level-spacing ratio distribution. Using interpolating functions between Poissonian-to-GOE and GOE-to-GUE, we have fitted the crossovers, to random matrix interpolating parameter ‘λ’. We find that once λ is properly scaled, the crossover behavior exhibits universality, in the sense that it becomes independent of lattice size in the large Hamiltonian-matrix dimension limit.