We construct the coordinate Bethe ansatz for all eigenstates of open $\mathrm{spin}\text{\ensuremath{-}}\frac{1}{2}$ XXZ chain that fulfill phantom roots criterion (PRC). Under PRC, Hilbert space splits into two invariant subspaces and there are sets homogeneous equations (BAE) to characterize in each case. propose vectors with chiral shocks span expand corresponding eigenstates. All factorized...

in this article we review an algebraic definition of the gyrogroup and a simplified version of the gyrovector space with two fundamental examples on the open ball of finite-dimensional euclidean space, which are the einstein and möbius gyrovector spaces. we introduce the structure of gyrovector space and the gyroline on the open convex cone of positive definite matrices and see its interest...