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Researchers in physical science persistently seek universal features instrongly interacting many-body systems. However, these traits often remainconcealed within highly complex observables like entanglement entropy (EE). Thenon-local essence of such observables renders experimental measurement andnumerical evaluation challenging. Thus, developing an accurate and convenientalgorithm to obtain these observables is imperative. In this work, aided byquantum Monte Carlo, we unveil an exponentially exploding coefficient ofvariation with system size in the direct calculation of EE, making theevaluation of EE inaccurate. We thus introduce a controllable incrementalalgorithm to solve this conundrum. We demonstrate the efficacy and convenienceof our algorithm by accurately evaluating the EE of a 2D Hubbardmodel.Moreover, our broadly adaptable technique can calculate numericallyunstable observables with exploding coefficient of variation, includingpartition function, entanglement spectra, and negativity in correlatedbosonic/fermionic systems. Precisely measuring these complex observables maymotivate theoretical and experimental

Controllable Incremental Algorithm for Entanglement Entropy in Quantum Monte Carlo Simulations