title: Entanglement, noise, and the cumulant expansion.
abstract: 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 log-normal 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 nth Rényi 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,⋯,10 Rényi entropies of the one-dimensional attractive Hubbard model. We use that data to extrapolate to the von Neumann (n=1) and n→∞ cases.
authors.affiliation: Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599-3255, USA.
authors.forename: Joaquín E
authors.initials: JE
authors.lastname: Drut
authors.affiliation: Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599-3255, USA.
authors.forename: William J
authors.initials: WJ
authors.lastname: Porter