Estimating the central charge from the Rényi entanglement entropy

Abstract

We calculate the von Neumann and R\'enyi bipartite entanglement entropy of the $O(2)$ model with a chemical potential on a $1+1$-dimensional Euclidean lattice with open and periodic boundary conditions. We show that the Calabrese-Cardy conformal field theory predictions for the leading logarithmic scaling of these entropies are consistent with a central charge $c=1$. This scaling survives the time-continuum limit and truncations of the microscopic degrees of freedom, modifications which allow us to connect the Lagrangian formulation to quantum Hamiltonians. At half-filling, the forms of the subleading corrections imposed by conformal field theory allow the determination of the central charge with an accuracy better than 2% for moderately sized lattices. We briefly discuss the possibility of estimating the central charge using quantum simulators.