  We propose a quantum Monte Carlo (QMC) scheme able to extract large-scale
data of entanglement entropy (EE) and its derivative with high precision and
low technical barrier. We avoid directly computing the overlap of two partition
functions within different spacetime manifolds and instead obtain them
separately via reweight-annealing scheme. The incremental process can be
designed along the path of real physical parameters in this frame, and all
intermediates are EEs of corresponding parameters, so the algorithm efficiency
is improved by more than $10^4$ of times. The calculation of EE becomes much
cheaper and simpler. It opens a way to numerically detect the novel phases and
phase transitions by scanning EE in a wide parameter-region in two and higher
dimensional systems. We then show the feasibility of using EE and its
derivative to find phase transition points and to probe novel phases.
