Bethe vectors for models based on the super-Yangian $Y(\mathfrak{gl}(m|n))$

TL;DR

This paper derives explicit formulas for Bethe vectors and their duals in models based on the super-Yangian $Y(rak{gl}(m|n))$, using recursion relations and super-trace formulas for specific cases.

Contribution

It introduces recursion relations and explicit expressions for Bethe vectors and their duals in super-Yangian models, expanding understanding of their structure.

Findings

Recursion relations for Bethe vectors in $Y(rak{gl}(2|1))$ and $Y(rak{gl}(1|2))$

Super-trace formulas for dual Bethe vectors

Explicit expressions for Bethe vectors and duals

Abstract

We study Bethe vectors of integrable models based on the super-Yangian $Y(\mathfrak{gl}(m|n))$. Starting from the super-trace formula, we exhibit recursion relations for these vectors in the case of $Y(\mathfrak{gl}(2|1))$ and $Y(\mathfrak{gl}(1|2))$. These recursion relations allow to get explicit expressions for the Bethe vectors. Using an antimorphism of the super-Yangian $Y(\mathfrak{gl}(m|n))$, we also construct a super-trace formula for dual Bethe vectors, and, for $Y(\mathfrak{gl}(2|1))$ and $Y(\mathfrak{gl}(1|2))$ super-Yangians, show recursion relations for them. Again, the latter allow us to get explicit expressions for dual Bethe vectors.