Universal term of Entanglement Entropy in the $π$-flux Hubbard model

Abstract

Researchers in physical science aim to uncover universal features in strongly interacting many-body systems, often hidden in complicated observables like entanglement entropy (EE). The non-local nature of EE makes it challenging to compute numerically, necessitating the development of an unbiased and convenient algorithm. In this paper, we use quantum Monte Carlo to reveal that the coefficient of variation in direct EE calculations increases exponentially with system size, leading to inaccuracies. To address this issue, we develop a power incremental algorithm and a technique for straightforwardly calculating the universal term of EE, successfully evaluating the EE of a 2D Hubbard model. Our numerical results demonstrate the consistency of the universal coefficient of EE from sharp corners at the Gross-Neveu quantum critical point and for free Dirac fermions. Our method can also be applied to other unstable observables, such as partition functions, entanglement spectra, and negativity, thereby fostering computational and theoretical progress.