Calculation of densities of states and spectral functions by Chebyshev recursion and maximum entropy

Journal Article · Wed Oct 01 04:00:00 EDT 1997 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.56.4822· OSTI ID:632560

Silver, R N; Roeder, H ^[1]

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1. MS B262 Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

We present an efficient algorithm for calculating spectral properties of large sparse Hamiltonian matrices such as densities of states and spectral functions. The combination of Chebyshev recursion and maximum entropy achieves high-energy resolution without significant roundoff error, machine precision, or numerical instability limitations. If controlled statistical or systematic errors are acceptable, CPU and memory requirements scale linearly in the number of states. The inference of spectral properties from moments is much better conditioned for Chebyshev moments than for power moments. We adapt concepts from the kernel polynomial method, a linear Chebyshev approximation with optimized Gibbs damping, to control the accuracy of Fourier integrals of positive nonanalytic functions. We compare the performance of kernel polynomial and maximum entropy algorithms for an electronic structure example. {copyright} {ital 1997} {ital The American Physical Society}

• OSTI ID: 632560
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 4 Vol. 56; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ALGORITHMS
DAMPING
DENSITY
ELECTRONIC STRUCTURE
ENTROPY
HAMILTONIANS
INSTABILITY
RECURSION RELATIONS
SPECTRAL FUNCTIONS