Efficient maximum entropy algorithms for electronic structure

摘要

Two Chebyshev recursion methods are presented for calculations with very large sparse Hamiltonians, the kernel polynomial method (KPM) and the maximum entropy method (MEM). If limited statistical accuracy and energy resolution are acceptable, they provide linear scaling methods for the calculation of physical properties involving large numbers of eigenstates such as densities of states, spectral functions, thermodynamics, total energies for Monte Carlo simulations and forces for molecular dynamics. KPM provides a uniform approximation to a DOS, with resolution inversely proportional to the number of Chebyshev moments, while MEM can achieve significantly higher, but non-uniform, resolution at the risk of possible artifacts. This paper emphasizes efficient algorithms.