Exactly solvable quantum spin ladders associated with the orthogonal and symplectic Lie algebras

TL;DR

This paper extends exactly solvable quantum spin ladder models to orthogonal and symplectic Lie algebras, demonstrating their integrability with arbitrary couplings and magnetic fields, thus broadening the class of solvable quantum systems.

Contribution

It introduces new integrable spin ladder models based on orthogonal and symplectic Lie algebras with explicit n-dependent symmetry.

Findings

Models exhibit orthogonal or symplectic symmetry with explicit n dependence.

Integrability is maintained for arbitrary XX-type rung couplings.

Models are valid under applied magnetic fields.

Abstract

We extend the results of spin ladder models associated with the Lie algebras $su(2^n)$ to the case of the orthogonal and symplectic algebras $o(2^n),\ sp(2^n)$ where n is the number of legs for the system. Two classes of models are found whose symmetry, either orthogonal or symplectic, has an explicit n dependence. Integrability of these models is shown for an arbitrary coupling of XX type rung interactions and applied magnetic field term.