KERNEL POLYNOMIAL APPROXIMATIONS FOR DENSITIES OF STATES AND SPECTRALFUNCTIONS

Chebyshev polynomial approximations are an efficient and numerically s table way to calculate properties of the very large Hamiltonians impor tant in computational condensed matter physics. The present paper deri ves an optimal kernel polynomial which enforces positivity of density of stales and spectral estimates, achieves the best energy resolution, and preserves normalization. This kernel polynomial method (KPM) is d emonstrated for electronic structure and dynamic magnetic susceptibili ty calculations. For tight binding Hamiltonians of Si, we show how to achieve high precision and rapid convergence of the cohesive energy an d vacancy formation energy by careful attention to the order of approx imation. For disordered XXZ-magnets, we show that the KPM provides a s impler and more reliable procedure for calculating spectral functions than Lanczos recursion methods. Polynomial approximations to Fermi pro jection operators are also proposed. (C) 1996 Academic Press, Inc.