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Chiral coordinate Bethe ansatz for phantom eigenstates in the open XXZ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>spin</mml:mi><mml:mtext>โ</mml:mtext><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:math> chain
We construct the coordinate Bethe ansatz for all eigenstates of the open $\mathrm{spin}\text{\ensuremath{-}}\frac{1}{2}$ XXZ chain that fulfill the phantom roots criterion (PRC). Under the PRC, the Hilbert space splits into two invariant subspaces and there are two sets of homogeneous Bethe ansatz equations (BAE) to characterize the subspaces in each โฆ