We derive exact expressions for the local entanglement entropy $\mathcal{E}$ 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 $\partial \mathcal{E}/\partial h$ and $\partial \mathcal{E}/\partial \mu$ 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.

• Received 22 June 2005

DOI:https://doi.org/10.1103/PhysRevLett.95.196406