Large-scale Exact Diagonalization of spin models with non-Abelian symmetries for the study of Many-Body Localization

In this thesis, we developed a massively parallel exact-diagonalization application to study effects of the non-Abelian symmetries namely the SU(2) symmetries on Many-body localization (MBL) in disordered 1D Heisenberg spin chains using the well known parallel libraries PETSc and SLEPc. Using the shift-invert spectral transformation technique, we study the eigenstates in the middle of the spectrum. We are able to look at the level statistics of the spin chain of sizes up to L = 26. Also, the code can calculate the Renyi entropy of the highly-excited eigenstates