Geometric entanglement for quantum critical spin chains belonging to the Ising and three-state Potts universality classes

Abstract The leading finite-size correction to the geometric entanglement per lattice site is investigated for the antiferromagnetic–ferromagnetic alternating Heisenberg model, quantum three-state Potts model in a transverse field and a spin-1/2 spin chain with the competing two-spin and three-spin interactions at criticality, belonging to the Ising and three-state Potts universality classes with the central charge c = 1 / 2 and c = 4 / 5 , respectively. Our results demonstrate that the leading finite-size correction coefficient is essentially the celebrated Affleck–Ludwig boundary entropy corresponding to a conformally invariant boundary condition, which in turn depends on the period of the translation-invariant separable states.