General build up of K+ basis and K+2 matrix in the diagonalization approach. Determination of Kramers configuration state functions. Issue 16 (23rd April 2018)

• Record Type: Journal Article
• Authors: Gall, Marián; Bučinský, Lukáš; Komorovsky, Stanislav
• Is Part Of: International journal of quantum chemistry. Volume 118:Issue 16(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-04-23
• Subjects: additivity -- algorithm -- binary tree -- diagonalization -- time reversal; Quantum chemistry -- Periodicals; 541.28
• DOI: 10.1002/qua.25638
• Languages: English
• ISSNs: 0020-7608

Abstract

Abstract: Algorithms to build the K ̂ + basis and K ̂ + 2 matrix representation to obtain the K ̂ + 2 Kramers configuration space functions (KCSFs) via diagonalization will be formally generalized to an arbitrary number of unpaired (open shell) fermions. Effective build up of the K ̂ + 2 matrix representation will be outlined (including threading and graphical processing unit parallelism) to subsequently obtain the KCSFs via calling external/numerical library routines for diagonalization. The effective build up of the K ̂ + 2 matrix representation relays on a binary tree search algorithm to allow evaluation the K ̂ i K ̂ j action on a given K ̂ + basis vector. The binary tree search avoids the treatment of zero K ̂ + 2 matrix elements which leads to an exponential acceleration. The implementation ( K ̂ + basis creation, K ̂ + 2 matrix representation, and K ̂ + 2 matrix diagonalization) will be done in an all in core and all at once manner, hence the available core memory sets the physical limits in practical applications. Memory limitations, sparsity of the K ̂ + 2 matrix, general case of n fermions in m spinors, and the application of KCSFs will be put into further perspective. Abstract : Additivity principle in time reversal symmetry introduces quantization in the many fermion relativistic case. Unlike spin symmetry, time reversal symmetry is not broken in the many fermion relativistic case. Generalization of the diagonalization algorithm is presented to produce Kramers Configuration State Functions. Binary tree search is employed to enable a fast generation of the required matrix representation for diagonalization.