Baxter's Q-operators for supersymmetric spin chains

TL;DR

This paper constructs Baxter's Q-operators for supersymmetric spin chains using quantum affine superalgebra structures, providing universal functional relations applicable to both lattice and field theory models.

Contribution

It explicitly develops six Q-operators for supersymmetric spin chains based on Uq( sl(2|1)), establishing their fusion relations and universality.

Findings

Six Q-operators obey fundamental fusion relations.

Functional relations between transfer matrices are derived.

Results are universal, applicable to lattice and quantum field models.

Abstract

We develop Yang-Baxter integrability structures connected with the quantum affine superalgebra Uq(\hat sl(2|1)). Baxter's Q-operators are explicitly constructed as supertraces of certain monodromy matrices associated with (q-deformed) bosonic and fermionic oscillator algebras. There are six different Q-operators in this case, obeying a few fundamental fusion relations, which imply all functional relations between various commuting transfer matrices. The results are universal in the sense that they do not depend on the quantum space of states and apply both to lattice models and to continuous quantum field theory models as well.