Oscillator Construction of su(n|m) Q-Operators

TL;DR

This paper introduces an algebraic oscillator-based method to construct Baxter Q-operators for supersymmetric su(n|m) spin chains, providing exact solutions without Bethe ansatz and revealing underlying algebraic structures.

Contribution

It extends previous su(n) constructions to supersymmetric su(n|m) cases using novel graded Yang-Baxter solutions, avoiding Bethe ansatz and connecting to hypercubic Hasse diagrams.

Findings

Constructed Q-operators for su(n|m) spin chains algebraically.

Provided exact solutions without Bethe ansatz.

Linked the construction to hypercubic Hasse diagrams.

Abstract

We generalize our recent explicit construction of the full hierarchy of Baxter Q-operators of compact spin chains with su(n) symmetry to the supersymmetric case su(n|m). The method is based on novel degenerate solutions of the graded Yang-Baxter equation, leading to an amalgam of bosonic and fermionic oscillator algebras. Our approach is fully algebraic, and leads to the exact solution of the associated compact spin chains while avoiding Bethe ansatz techniques. It furthermore elucidates the algebraic and combinatorial structures underlying the system of nested Bethe equations. Finally, our construction naturally reproduces the representation, due to Z. Tsuboi, of the hierarchy of Baxter Q-operators in terms of hypercubic Hasse diagrams.