  In this work we consider the Kitaev Toric Code with specific open boundary
conditions. Such a physical system has a highly degenerate ground state
determined by the degrees of freedom localised at the boundaries. We can write
down an explicit expression for the ground state of this model. Based on this,
the entanglement properties of the model are studied for two types of
bipartition: one, where the subsystem A is completely contained in B; and the
second, where the boundary of the system is shared between A and B. In the
former configuration, the entanglement entropy is the same as for the periodic
boundary condition case, which means that the bulk is completely decoupled from
the boundary on distances larger than the correlation length. In the latter,
deviations from the torus configuration appear due to the edge states and lead
to an increase of the entropy. We then determine an effective theory for the
boundary of the system. In the case where we apply a small magnetic field as a
perturbation the degrees of freedom on the boundary acquire a dispersion
relation. The system can there be described by a Hamiltonian of the Ising type
with a generic spin-exchange term.
