Specialised NMR spin-cluster symmetry chains under SU(m) X Ln group dualities: Role of democratic recoupling and projective geometric mapping from SU(m) p-tuples onto Γ[γ](v: Ln), or onto Γ(v: Ln↓G), for 6⩽n-fold cage clusters

F.p Temme

Physica A: Statistical Mechanics and its Applications, 1994, vol. 202, issue 3, 595-623

Abstract: The inherent nature of the dual group spin algebras for NMR spin clusters over their associated carrier spaces is examined in the context of scalar invariants (SIs). The [A]n(SU(m)×Ln↓G) aspects of [AX]n cage spin biclusters furnish these SI forms, and focus our attention on their part in the Ln-induced representational hierarchy for democratic recoupling in NMR spin-dynamical formalisms. The purpose of the present work is to examine the nature of the specialised symmetry chains, their mappings and SU2-distinct {H̃v} carrier subspaces, especially for non-“magnetically equivalent” (non-ME) supermolecular spin biclusters in the 6 ⩽ n ⩽ 20, 60, 2160 limit. A hierarchy of intracluster {Jij} interactions ensures that the Ln-group and its graph-theoretical schemata dominate the spin algebra. These Heisenberg aspects arise from the bilinear terms of the zeroth Hamiltonian, Ĥ0. Their dominance highlights certain contrasts with conventional unitary-algebras and Wigner unit-operator properties.

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:202:y:1994:i:3:p:595-623

DOI: 10.1016/0378-4371(94)90481-2

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