Entanglement, noise, and the cumulant expansion

We put forward a simpler and improved variation of a recently proposed method to overcome the signal-to-noise problem found in Monte Carlo calculations of the entanglement entropy of interacting fermions. The present method takes advantage of the approximate lognormal distributions that characterize the signal-to-noise properties of other approaches. In addition, we show that a simple rewriting of the formalism allows circumvention of the inversion of the restricted one-body density matrix in the calculation of the $n$-th R\'enyi entanglement entropy for $n>2$. We test our technique by implementing it in combination with the hybrid Monte Carlo algorithm and calculating the $n=2,3,4, \dots, 10$ R\'enyi entropies of the 1D attractive Hubbard model. We use that data to extrapolate to the von Neumann ($n=1$) and $n\to\infty$ cases.