2011/02/18 by Myrta Grüning, Grüning, Myrta, Andrea Marini +3 · 1 citation
Physics and Astronomy · Chemistry · #Quantum, superfluid, helium dynamics #Advanced NMR Techniques and Applications #Advanced Chemical Physics Studies
paper · pdf · doi:10.48550/arxiv.1102.3909
The treatment of the Random-Phase Approximation Hamiltonians, encountered in\ndifferent frameworks, like Time-Dependent Density Functional Theory or\nBethe-Salpeter equation, is complicated by their non-Hermicity. Compared to\ntheir Hermitian Hamiltonian counterparts, computational methods for the\ntreatment of non-Hermitian Hamiltonians are often less efficient and less\nstable, sometimes leading to the breakdown of the method. Recently [Gr "uning\net al. Nano Lett. bf 8, 2820 (2009)], we have identified that such\nHamiltonians are usually pseudo-Hermitian. Exploiting this property, we have\nimplemented an algorithm of the Lanczos type for random-Phase Approximation\nHamiltonians that benefits from the same stability and computational load as\nits Hermitian counterpart, and applied it to the study of the optical response\nof carbon nanotubes. We present here the related theoretical grounds and\ntechnical details, and study the performance of the algorithm for the\ncalculation of the optical absorption of a molecule within the Bethe-Salpeter\nequation framework.\n