Modified algebraic Bethe ansatz for XXZ chain on the segment - I: Triangular cases

The modified algebraic Bethe ansatz, introduced by Cramp6 and the author [8], is used to characterize the spectral problem of the Heisenberg XXZ spin-1/2 chain on the segment with lower and upper triangular boundaries. The eigenvalues and the eigenvectors are conjectured. They are characterized by a set of Bethe roots with cardinality equal to N the length of the chain and which satisfies a set of Bethe equations with an additional term. The conjecture follows from exact results for small chains. We also present a factorized formula for the Bethe vectors of the Heisenberg XXZ spin-1/2 chain on the segment with two upper triangular boundaries. (C) 2015 The Author. Published by Elsevier B.V.