Baxter Q-operator for graded SL(2|1) spin chain

TL;DR

This paper extends the Baxter Q-operator method to integrable superspin chains with SL(2|1) symmetry, enabling spectrum analysis without relying on a pseudovacuum, and offers a framework for supergroup-based models.

Contribution

It introduces a novel construction of Baxter Q-operators for SL(2|1) superspin chains, generalizing the method beyond traditional Bethe Ansatz approaches.

Findings

Derived the eigenspectrum of the SL(2|1) superspin chain.

Established functional relations and TQ-relations for Q-operators.

Proposed a generalization to higher-rank supergroup models.

Abstract

We study an integrable noncompact superspin chain model that emerged in recent studies of the dilatation operator in the N=1 super-Yang-Mills theory. It was found that the latter can be mapped into a homogeneous Heisenberg magnet with the quantum space in all sites corresponding to infinite-dimensional representations of the SL(2|1) group. We extend the method of the Baxter Q-operator to spin chains with supergroup symmetry and apply it to determine the eigenspectrum of the model. Our analysis relies on a factorization property of the R-operators acting on the tensor product of two generic infinite-dimensional SL(2|1) representations. It allows us to factorize an arbitrary transfer matrix into a product of three `elementary' transfer matrices which we identify as Baxter Q-operators. We establish functional relations between transfer matrices and use them to derive the TQ-relations for the Q-operators. The proposed construction can be generalized to integrable models based on supergroups of higher rank and, in distinction to the Bethe Ansatz, it is not sensitive to the existence of the pseudovacuum state in the quantum space of the model.