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Department of Physics, Göteborg University, SE 412 96 Göteborg, Sweden.
We derive exact expressions for the local entanglement entropy epsilon 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 delta epsilon/delta h and delta epsilon/delta 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.
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