  We calculate planar tree level one-point functions of non-protected operators
in the defect conformal field theory dual to the D3-D5 brane system with k
units of the world volume flux. Working in the operator basis of Bethe
eigenstates of the Heisenberg XXX_{1/2} spin chain we express the one-point
functions as overlaps of these eigenstates with a matrix product state. For k=2
we obtain a closed expression of determinant form for any number of
excitations, and in the case of half-filling we find a relation with the N\'eel
state. In addition, we present a number of results for the limiting case of
infinite k.
