On-the-fly exact diagonalization solver for quantum electronic models

Abstract: We propose a distinct numerical approach to effectively solve the problem of partial diagonalization of the super-large-scale quantum electronic Hamiltonian matrices. The key ingredients of our scheme are the new method for arranging the basis vectors in the computer's RAM and the algorithm allowing not to store a matrix in RAM, but to regenerate it on-the-fly during diagonalization procedure. This scheme was implemented in the program, solving the Anderson impurity model in the framework of dynamical mean-field theory (DMFT). The DMFT equations for electronic Hamiltonian with 18 effective orbitals that corresponds to the matrix with the dimension of 2.4 * 10^9 were solved on the distributed memory computational cluster.