Year: 2016
Communications in Computational Physics, Vol. 19 (2016), Iss. 1 : pp. 192–204
Abstract
We devise an efficient algorithm for the symbolic calculation of irreducible angular momentum and spin (LS) eigenspaces within the $n$-fold antisymmetrized tensor product $Λ^n$$V_u$, where n is the number of electrons and $u$ = s,p,d,··· denotes the atomic subshell. This is an essential step for dimension reduction in configuration-interaction (CI) methods applied to atomic many-electron quantum systems. The algorithm relies on the observation that each $L_z$ eigenstate with maximal eigenvalue is also an $L^2$ eigenstate (equivalently for $S_z$ and $S^2$ ), as well as the traversal of LS eigenstates using the lowering operators $L_−$ and $S_−$. Iterative application to the remaining states in $Λ^n$$V_u$ leads to an implicit simultaneous diagonalization. A detailed complexity analysis for fixed $n$ and increasing subshell number $u$ yields run time $\mathcal{O}$($u^{3n−2}$). A symbolic computer algebra implementation is available online.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.281014.190615a
Communications in Computational Physics, Vol. 19 (2016), Iss. 1 : pp. 192–204
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 13