Effective su_q(2) models and polynomial algebras for fermion-boson Hamiltonians

TL;DR

This paper explores the relationship between su(2)+h3 interaction Hamiltonians and q-su(2) quantum algebras, introducing nonlinear models and analyzing their integrability and physical parameter connections.

Contribution

It introduces q-su(2) analogues of known fermion-boson models and analyzes their algebraic structure and integrability properties.

Findings

q-su(2) models closely relate to fermion-boson Hamiltonians

Polynomial algebras reveal integrability properties

Connections between algebra parameters and physical system parameters

Abstract

Schematic su(2)+h3 interaction Hamiltonians, where su(2) plays the role of the pseudo-spin algebra of fermion operators and h3 is the Heisenberg algebra for bosons, are shown to be closely related to certain nonlinear models defined on a single quantum algebra q-su(2) of quasifermions. In particular, q-su(2) analogues of the Da Providencia-Schutte and extended Lipkin models are presented. The connection between q and the physical parameters of the fermion-boson system is analysed, and the integrability properties of the interaction Hamiltonians are discussed by using polynomial algebras.