  We derive exact expressions for the local entanglement entropy E in the
ground state of the one-dimensional Hubbard model at a quantum phase transition
driven by a change in magnetic field h or chemical potential u. The leading
divergences of dE/dh and dE/du are shown to be directly related to those of the
zero-temperature spin and charge susceptibilities. Logarithmic corrections to
scaling signal a change in the number of local states accessible to the system
as it undergoes the transition.
