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Universal logarithmic terms in the entanglement entropy appear at quantumcritical points (QCPs) in one dimension (1D) and have been predicted in 2D atQCPs described by 2D conformal field theories. The entanglement entropy in astrip geometry at such QCPs can be obtained via the "Shannon entropy" of a 1Dspin chain with open boundary conditions. The Shannon entropy of the XXZ chainis found to have a logarithmic term that implies, for the QCP of thesquare-lattice quantum dimer model, a logarithm with universal coefficient $\pm0.25$. However, the logarithm in the Shannon entropy of the transverse-fieldIsing model, which corresponds to entanglement in the 2D Ising conformal QCP,is found to have a singular dependence on replica or R\'enyi index resultingfrom flows to different boundary conditions at the entanglement cut.

Logarithmic terms in entanglement entropies of 2D quantum critical points and Shannon entropies of spin chains