Parallel implementation of the Krylov subspace techniques for unitary time evolution of disordered quantum strongly correlated systems

The study of dynamics of quantum systems proposes both a highly interesting framework to current research in physics and a demanding numerical and computational task. Disordered systems and those that mimic the dynamical properties inherent to disorder, constitute a stepping stone to reach further understanding of quantum electronic and energy transport along with other properties that can be used to shed light to diverse topics in both theoretical and applied physics. We have developed an application and implemented parallel algorithms using the Message Passing Interface in order to provide a computational framework suitable for massively parallel supercomputers to study the dynamics of such physical systems. We used high-performing libraries such as PETSc/SLEPc combined with High Performance Computing approaches in order to study systems whose subspace dimension is constituted by over 9 billion independent quantum states. Moreover, we provide descriptions on the parallel approach used for the two most important stages of the computation: constructing a matrix representation for a generic Hamiltonian operator and the time evolution of the system by means of the Krylov subspace methods. We have enabled the application and successfully performed simulations using three different supercomputers (on both SISSA and CINECA computational frameworks) and provide results to evaluate the overall performance of the application, as well as physical results from the dynamics of a quasi-disordered system under the Aubry-André model.