Baxter's Q-operators and operatorial Backlund flow for quantum (super)-spin chains

TL;DR

This paper develops an operatorial framework for Baxter's TQ-relations and Bäcklund flow in quantum super-spin chains, enabling systematic derivation of nested Bethe ansatz equations for integrable models.

Contribution

It introduces a general operatorial form of Baxter's relations and defines the full set of Q- and T-operators for inhomogeneous rational super-spin chains with twisted boundary conditions.

Findings

Explicit construction of Q- and T-operators at all nesting levels

Systematic derivation of nested Bethe ansatz equations

Generalization of character identities for supergroups

Abstract

We propose the operatorial form of Baxter's TQ-relations in a general form of the operatorial B\"acklund flow describing the nesting process for the inhomogeneous rational gl(K|M) quantum (super)spin chains with twisted periodic boundary conditions. The full set of Q-operators and T-operators on all levels of nesting is explicitly defined. The results are based on a generalization of the identities among the group characters and their group co-derivatives with respect to the twist matrix, found by one of the authors and P.Vieira [V.Kazakov and P.Vieira, JHEP 0810 (2008) 050 [arXiv:0711.2470]]. Our formalism, based on this new "master" identity, allows a systematic and rather straightforward derivation of the whole set of nested Bethe ansatz equations for the spectrum of quantum integrable spin chains, starting from the R-matrix.