Dual algebraic structures for the two-level pairing model

TL;DR

This paper establishes duality relations between Hamiltonians and basis schemes in two-level pairing models, unifying bosonic and fermionic systems with arbitrary degeneracies, and compares their quantum phase transitions.

Contribution

It introduces a unified framework for dual algebraic structures in two-level pairing models applicable to both bosonic and fermionic systems with unequal degeneracies.

Findings

Duality relations explicitly derived for Hamiltonians and basis schemes.

Unified formulation valid for bosonic and fermionic systems.

Comparison of quantum phase transitions in bosonic and fermionic cases.

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.