Entanglement scaling in the one-dimensional Hubbard model at criticality

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 mu. The leading divergences of partial derivative E/partial derivative h and partial derivative E/partial derivative mu 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.