title: Accuracy of topological entanglement entropy on finite cylinders.
abstract: Topological phases are unique states of matter which support nonlocal excitations which behave as particles with fractional statistics. A universal characterization of gapped topological phases is provided by the topological entanglement entropy (TEE). We study the finite size corrections to the TEE by focusing on systems with a Z2 topological ordered state using density-matrix renormalization group and perturbative series expansions. We find that extrapolations of the TEE based on the Renyi entropies with a Renyi index of n≥2 suffer from much larger finite size corrections than do extrapolations based on the von Neumann entropy. In particular, when the circumference of the cylinder is about ten times the correlation length, the TEE obtained using von Neumann entropy has an error of order 10(-3), while for Renyi entropies it can even exceed 40%. We discuss the relevance of these findings to previous and future searches for topological ordered phases, including quantum spin liquids.
authors.affiliation: Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA.
authors.forename: Hong-Chen
authors.initials: HC
authors.lastname: Jiang
authors.affiliation: Physics Department, University of California, Davis, California 95616, USA.
authors.forename: Rajiv R P
authors.initials: RR
authors.lastname: Singh
authors.affiliation: Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA.
authors.forename: Leon
authors.initials: L
authors.lastname: Balents