An attempt to calculate energy eigenvalues in quantum systems of large sizes

We report an attempt to calculate energy eigenvalues of large quantum syste ms by the diagonalization of an effectively truncated Hamiltonian matrix. F or this purpose we employ a specific way to systematically make a set of or thogonal states from a trial wavefunction and the Hamiltonian. In compariso n with the Lanczos method, which is quite powerful if the size of the syste m is within the memory capacity of computers, our method requires much less memory resources at the cost of the extreme accuracy. In this paper we dem onstrate that our method works well in the systems of one-dimensional frust rated spins up to 48 sites, of bosons on a chain up to 32 sites and of ferm ions on a ladder up to 28 sites. We will see this method enables us to stud y eigenvalues of these quantum systems within reasonable accuracy.