The Spin Quartet Γ8 × (e + t 2) System and the Symplectic Group Sp(4)

Arnout Ceulemans
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Arnout Ceulemans: KU Leuven

Chapter Chapter 6 in The Theory of the Jahn-Teller Effect, 2022, pp 131-165 from Springer

Abstract: Abstract The Jahn-Teller instability of the spin quartet degeneracy corresponds to the Γ8 × (e + t 2) problem in cubic symmetry, and to the Γ8 × h problem in icosahedral symmetry. It may be surprising that the treatment of this problem precedes the orbital triplet case in the next chapter. However because of Kramers degeneracy for spin states, the quartet effectively reduces to a two-level problem involving two unbreakable Kramers doublets. As such it has much in common with the orbital doublet problem, but also forms a launching path towards the triplet problem, which involves the same Jahn-Teller modes but requires additional group-theoretical concepts. Three cases are examined: the case of degenerate coupling with spherical symmetry, and the subproblems Γ8 × e and Γ8 × t 2. The spherical system is characterized by the Lie algebras of the symplectic group Sp(4), and the isomorphic orthogonal group SO(5). Dynamic equations are derived in the Bargmann formalism, and their correspondence with the standard E × e model is discussed.

Date: 2022
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DOI: 10.1007/978-3-031-09528-3_6

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