Dual algebraic structures for the two-level pairing model

Abstract

Duality relations are explicitly established relating the Hamiltonians and basis classification schemes associated with the number-conserving unitary and number-nonconserving quasispin algebras for the two-level system with pairing interactions. These relations are obtained in a unified formulation for both bosonic and fermionic systems, with arbitrary and, in general, unequal degeneracies for the two levels. Illustrative calculations are carried out comparing the bosonic and fermionic quantum phase transitions.

34 pages, 5 figures; published in J. Phys. A

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• Intrinsic operators for the translationally-invariant many-body problem
• Rotation and vibration in tetraquarks
• Spectral fluctuations in the interacting boson model
• Algebraic solutions for $o(12)\leftrightarrow u(2)\otimes u(10)$ quantum phase transitions in the proton-neutron interacting boson model