Extracting subleading corrections in entanglement entropy at quantum phase transitions

We systematically investigate the finite size scaling behavior of the Rényi entanglement entropy (EE) of several representative 2d quantum many-body systems between a subregion and its complement, with smooth boundaries as well as boundaries with corners. In order to reveal the subleading correction, we investigate the quantity “subtracted EE” Sˢ (l) = S (2l) - 2S (l) Ss (l) =S (2l) −2S (l) for each model, which is designed to cancel out the leading perimeter law. We find that (1) for a spin-1/2 model on a 2d square lattice whose ground state is the Neel order, the coefficient of the logarithmic correction to the perimeter law is consistent with the prediction based on the Goldstone modes; (2) for the (2+1) d (2+1) d O (3) Wilson-Fisher quantum critical point (QCP), realized with the bilayer antiferromagnetic Heisenberg model, a logarithmic subleading correction exists when there is sharp corner of the subregion, but for subregion with a smooth boundary our data suggests the absence of the logarithmic correction to the best of our efforts; (3) for the (2+1) d (2+1) d SU (2) J-Q ₂ 2 and J-Q ₃ 3 model for the deconfined quantum critical point (DQCP), we find a logarithmic correction for the EE even with smooth boundary.