  Recently the ground state and some excited states of the half-filled case of
the 1d Hubbard model were discussed for an open chain with L sites. Authors
considered the case when the boundary site has a negative chemical potential -p
and the Hubbard coupling U is positive. They have shown by an analytic method
that when p is larger than the transfer integral some of the ground-state
solutions of the Bethe ansatz equations become complex-valued. They have found
that there is a surface phase transition at some critical value p_c; when p <
p_c all the charge excitations have the gap for this case, while there exists a
massless charge mode when p > p_c. To find whether this surface phase
transition is of the first order or of the second order we have used the
entanglement entropy concept. The entropy and its derivative has a
discontinuity there, so this transition is of the first order.
