Spin chains from dynamical quadratic algebras

TL;DR

This paper introduces a method to construct integrable quantum spin chains with position-dependent interactions influenced by dynamical quadratic algebras, expanding the framework for modeling complex spin systems.

Contribution

It extends the theory of quadratic reflection-type algebras to include dynamical and non-dynamical cases, enabling new integrable spin chain models with non-local spin dependence.

Findings

Constructed integrable spin chains with position-dependent interactions.

Unified treatment of non-dynamical, semidynamical, and dynamical quadratic algebras.

Potential applications in modeling complex quantum systems.

Abstract

We present a construction of integrable quantum spin chains where local spin-spin interactions are weighted by ``position''-dependent potential containing abelian non-local spin dependance. This construction applies to the previously defined three general quadratic reflection-type algebras: respectively non-dynamical, semidynamical, fully dynamical.