Multiple Actions of the Monodromy Matrix in gl(2|1)-Invariant Integrable Models

Abstract

Abstract. We study gl(2|1) symmetric integrable models solvable by the nested algebraic Bethe ansatz. Using explicit formulas for the Bethe vectors we derive the actions of the monodromy matrix entries onto these vectors. We show that the result of these actions is a finite linear combination of Bethe vectors. The obtained formulas open a way for studying scalar products of Bethe vectors.

Current presentation for the super-Yangian double $ DY(\mathfrak{gl}(m\vert n))$ and Bethe vectors

“…Recently similar results were obtained for the models with gl(1|2) and gl(2|1) superalgebras in [18,19]. In these works the explicit formulas for the Bethe vectors and the action formulas were essentially used [20,21].…”

“…Let us give explicit formulas for a particular case of (dual) Bethe vectors B(t),B(t), C(t) andĈ(t) defined by the formulas (5.20), (5.28) and related to the Yangian double DY (gl(2|1)). Then, we have two sets of Bethe parameterst ℓ with cardinalities #t ℓ = r ℓ , ℓ = 1, 2, which we rename ast 1 ≡ū and t 2 ≡v with cardinalities r 1 = a and r 2 = b. Formulas (3.14), (3.15), (3.22) and (3.23) for these Bethe vectors acquire the form [18,19,20] to calculate the form factors of the monodromy matrix elements in the supersymmetric quantum integrable models associated with the super-Yangian Y (gl(2|1)).…”

Bethe Vectors for Composite Models with gl(2|1) and gl(1|2) Supersymmetry

“…The method of calculation was straightforward. We used the known action of the monodromy matrix elements on the Bethe vectors [12].…”

Form factors of the monodromy matrix entries ingl(2|1)-invariant integrable models

“…The explicit formulas for the action the operators T ij (z) onto Bethe vectors were derived in [42].…”