arXiv:1611.00943 · Symmetry Integrability and Geometry Methods and Applications

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

Jan Fuksa

Published Mar 13, 2017• 5 citations

Abstract

Supersymmetric composite generalized quantum integrable models solvable by the algebraic Bethe ansatz are studied.Using a coproduct in the bialgebra of monodromy matrix elements and their action on Bethe vectors, formulas for Bethe vectors in the composite models with supersymmetry based on the super-Yangians Y [gl(2|1)] and Y [gl(1|2)] are derived.

DOI: 10.3842/sigma.2017.015

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arXiv:1611.00943 · Symmetry Integrability and Geometry Methods and Applications

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

Jan Fuksa

Published Mar 13, 2017• 5 citations

arXiv HTML PDF

Abstract

DOI: 10.3842/sigma.2017.015

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We find Bethe vectors for quantum integrable models associated with the supersymmetric Yangians

Y(\mathfrak{gl}(m|n)

in terms of the current generators of the Yangian double

DY(\mathfrak{gl}(m|n))

. More specifically, we use the method of projections onto intersections of different type Borel subalgebras in this infinite dimensional algebra to construct the Bethe vectors. Calculating these projection the supersymmetric Bethe vectors can be expressed through matrix elements of the universal monodromy matrix elements. Using two different but isomorphic current realizations of the Yangian double

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Bethe vectors in integrable models based on the super-Yangian

Y(\mathfrak{gl}(m|n))

We find Bethe vectors for quantum integrable models associated with the supersymmetric Yangians

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DY(\mathfrak{gl}(m|n))

DY(\mathfrak{gl}(m|n))

we obtain two different presentations for the Bethe vectors. These Bethe vectors are also shown to obey some recursion relations which prove their equivalence.