An attempt to calculate energy eigenvalues in quantum systems of large sizes (operator-variational approach)

Abstract

We report a method to calculate energy eigenvalues of large quantum systems based on the variational method. For this purpose we develop a specific way to systematically make a set of orthogonal states from a trial state and the Hamiltonian. In our method, compared with the Lanczos method, much less memory resource of computers is necessary to obtain numerical results on large systems with satisfying accuracy. We have demonstrated that the method is applicable to some spin systems, boson systems and fermions systems, where we studied the ground states of them. In this paper we discuss some details of the method and present results on the excited states of the orthogonal dimer spin system in two dimensions.