Work

Exactly solvable inhomogeneous periodic quantum spin chain from q-ultraspherical polynomials at roots of unity

Year: 2025

Type: article

Abstract: We present a closed inhomogeneous quantum XX spin chain on the periodic integer lattice $$\mathbb {Z}_m$$ which is diagonalized by means of Slater determinants built from Rogers’ q-ultraspherical polynomials with $$q^m=1$$ . The hermiticity of our periodic quantum spin Hamiltonian encodes a discrete orthogonality relation for these q-ultraspherical polynomials that is of a type studied previously by Spiridonov and Zhedanov.

Source: Letters in Mathematical Physics

DOI: 10.1007/s11005-025-02022-y

Authors: Andreo Cazares, Jan Felipe van Diejen

Institution: University of Talca

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funder: Fondo Nacional de Desarrollo Científico y Tecnológico