Matrix Coordinate Bethe Ansatz: Applications to XXZ and ASEP models

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We present the construction of the full set of eigenvectors of the open ASEP and XXZ models with special constraints on the boundaries.

• The method combines both recent constructions of coordinate Bethe Ansatz and the old method of matrix Ansatz specific to the ASEP.
• This "matrix coordinate Bethe Ansatz" can be viewed as a non-commutative coordinate Bethe Ansatz, the non-commutative part being related to the algebra appearing in