Inhomogeneous six-vertex model with domain wall boundary conditions and Bethe ansatz

In this note, we consider the six-vertex model with domain wall boundary conditions, defined on an M × M lattice, in the inhomogeneous case where the partition function depends on 2 M inhomogeneities λ_j and μ_k. For a particular choice of the set of λ_j we find a new determinant representation for the partition function, which allows evaluation of the bulk free energy in the thermodynamic limit. This provides a new connection between two types of determinant formulas. We also show in a special case that spin correlations on the horizontal line going through the center coincide with the ones for periodic boundary conditions.