Extracting subleading corrections in entanglement entropy at quantum phase transitions

We systematically investigate the finite size scaling behavior of the R\'enyientanglement entropy (EE) of several representative 2d quantum many-bodysystems between a subregion and its complement, with smooth boundaries as wellas boundaries with corners. In order to reveal the subleading correction, weinvestigate the quantity ``subtracted EE" $S^s(l) = S(2l) - 2S(l)$ for eachmodel, which is designed to cancel out the leading perimeter law. We find that$\mathbf{(1)}$ for a spin-1/2 model on a 2d square lattice whose ground stateis the Neel order, the coefficient of the logarithmic correction to theperimeter law is consistent with the prediction based on the Goldstone modes;$\mathbf{(2)}$ for the $(2+1)d$ O(3) Wilson-Fisher quantum critical point(QCP), realized with the bilayer antiferromagnetic Heisenberg model, alogarithmic subleading correction exists when there is sharp corner of thesubregion, but for subregion with a smooth boundary our data suggests theabsence of the logarithmic correction to the best of our efforts;$\mathbf{(3)}$ for the $(2+1)d$ SU(2) J-Q$_2$ and J-Q$_3$ model for thedeconfined quantum critical point (DQCP), we find a logarithmic correction forthe EE even with smooth boundary.