ORDER-N METHOD TO CALCULATE THE LOCAL-DENSITY OF STATES

We present a rigorous and general method to extract the local density of states rho(i)(omega) of a system from its time response to a specif ied external perturbation. This method is order-N when the matrix is s parse. In a single run it gives rho(i)(omega), rho(i)(2 omega), ..., r ho(i)(n omega), ... concurrently, which enhances the total efficiency by two decades. Application to a lattice-dynamics problem of 4096 SiC particles in a supercell with a dynamical matrix generated from an app ropriate interatomic potential shows excellent agreement with exact ph onon-dispersion calculations; the accelerated algorithm yields a full local density of states spectrum for each supercell k point in 15 min on a desktop workstation. Results showing the effects of an antisite-p air defect are given for which methods requiring lattice periodicity c annot be used.