Error estimation of recursive orthogonal polynomial expansion method for large Hamiltonian system

Recursive polynomial expansion method is an efficient scheme to evaluate Green functions for large systems without direct diagonalization of the Hamiltonian. It is based on a polynomial expansion of the Green function, and has many advantages compared with other methods. However, there are little reports on its error estimations. In this paper, the cut-off error of the method is estimated analytically, which results from the truncation of expansion at finite orders. It is found that the error is inversely proportional to the number of expansion order N except for the singular points for the system with point spectrum. For the system with continuous spectrum, the error is inversely proportional to N^3/2 and decreases much faster in terms of the expansion order.