Precise computation of universal terms for the entanglement entropy at 2+1-dimensional quantum phase transitions

The sub-leading logarithmic term to the entanglement entropy (EE) is difficult to compute, yet it reveals universal characteristics of quantum critical points (QCPs). Motivated by recent advances in incremental methods for the stable calculation of EE in (2+1)-dimension quantum many-body systems, we apply and extend this technique to extract the universal corner contribution to the EE in a parameter path from Ising to Gaussian QCPs, where in the latter case, there exists an analytic value to benchmark. Our approach cancels the area-law term in the quantum Monte Carlo simulation and directly reveals the sub-leading logarithmic term. We compute the EE in a (2+1)D square-lattice transverse-field Ising model augmented with a four-body interaction term, across a parameter path from Ising QCP to the Gaussian fixed point and eventually first-order transition. The consistent values we obtain for the universal logarithmic coefficient along this path demonstrate the reliability of our approach in extracting the challenging entanglement properties, and provide the long missing link of these universal values from the exactly solvable limit to the strongly correlated regime.