QQ-system and Weyl-type transfer matrices in integrable SO(2r) spin chains

TL;DR

This paper develops a comprehensive QQ-system for SO(2r) spin chains, deriving new formulas for transfer matrices in various representations, and confirms consistency with recent Q-operator proposals.

Contribution

It introduces a complete QQ-system for D_r symmetric spin chains and derives Weyl-type formulas for transfer matrices in all fundamental representations.

Findings

Derived new Weyl-type formulas for transfer matrices.

Confirmed consistency with recent Q-operator proposals.

Verified relations explicitly at small finite length.

Abstract

We propose the full system of Baxter Q-functions (QQ-system) for the integrable spin chains with the symmetry of the $D_r$ Lie algebra. We use this QQ-system to derive new Weyl-type formulas expressing transfer matrices in all symmetric and antisymmetric (fundamental) representations through $r+1$ basic Q-functions. Our functional relations are consistent with the Q-operators proposed recently by one of the authors and verified explicitly on the level of operators at small finite length.