  We show that infinite Matrix Product States (MPS) constructed from conformal
field theories can describe ground states of one-dimensional critical systems
with open boundary conditions. To illustrate this, we consider a simple
infinite MPS for a spin-1/2 chain and derive an inhomogeneous open
Haldane-Shastry model. For the spin-1/2 open Haldane-Shastry model, we derive
an exact expression for the two-point spin correlation function. We also
provide an SU($n$) generalization of the open Haldane-Shastry model and
determine its twisted Yangian generators responsible for the highly degenerate
multiplets in the energy spectrum.
