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

Abstract

The modified algebraic Bethe ansatz, introduced by Crampé and the author [8], is used to characterize the spectral problem of the Heisenberg XXZ spin-$\frac{1}{2}$ 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-$\frac{1}{2}$ chain on the segment with two upper triangular boundaries.

V2: published version, some typos were corrected and one remark (5.2) on scalar product was added

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Cited by in corpus (5)

• Modified algebraic Bethe ansatz for XXZ chain on the segment - II - general cases
• Bethe states of the XXZ spin-1/2 chain with arbitrary boundary fields
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I
• Algebraic Bethe Ansatz for the XXZ Gaudin Models with Generic Boundary
• Algebraic Bethe ansatz for the totally asymmetric simple exclusion process with boundaries