On the resolution of the filter diagonalization method

We present a convergence study of the filter diagonalization method. Test calculations on model systems are performed with the goal to find the minimum signal length necessary to resolve eigenenergies. For these model systems we find analytic expressions for the Hamiltonian and overlap matrix elements for a few different filtering functions. The matrix elements are therefore exact within the numerical precision of the calculations. The relationship between the filter diagonalization method and the uncertainty principle is investigated. The effect of varying the density of states is studied. The results obtained suggest that the resolution of the filter diagonalization method sometimes can be improved by using high numerical precision in the calculations. For a general case the resolution of the filter diagonalization method is limited by the average density of states and is affected by the structure of the eigenvalue spectrum.