Accuracy of topological entanglement entropy on finite cylinders

Abstract

Topological phases are unique states of matter which support non-local 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 $Z_2$ topological ordered state using density-matrix renormalization group (DMRG) and perturbative series expansions. We find that extrapolations of the TEE based on the Renyi entropies with Renyi index $n\ge 2$ 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.

8 pages, 9 figures

References in corpus (9)

• Non-Abelian Anyons and Topological Quantum Computation
• Identifying Topological Order by Entanglement Entropy
• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
• Entanglement at a Two-Dimensional Quantum Critical Point: a Numerical Linked Cluster Expansion Study
• Thermodynamic singularities in the entanglement entropy at a 2D quantum critical point
• Topological phases and topological entropy of two-dimensional systems with finite correlation length
• Probing topological order with Rényi entropy
• Phenomenological Z_2 lattice gauge theory of the spin-liquid state of the kagome Heisenberg antiferromagnet
• Finite size effects in the Z_2 spin liquid on the kagome lattice

Cited by in corpus (12)

• Quantum Spin Liquids
• Quantum entanglement in condensed matter systems
• Prediction of Toric Code Topological Order from Rydberg Blockade
• Diagnostics of mixed-state topological order and breakdown of quantum memory
• Unifying Kitaev magnets, kagome dimer models and ruby Rydberg spin liquids
• Z2 topological liquid of hard-core bosons on a kagome lattice at 1/3 filling
• Magnetization of the spin-1/2 Heisenberg antiferromagnet on the triangular lattice
• Unusual Corrections to Scaling and Convergence of Universal Renyi Properties at Quantum Critical Points
• Entanglement in a second order topological insulator on a square lattice
• On Quantum Entanglement in Topological Phases on a Torus
• SU(4) topological RVB spin liquid on the square lattice
• ParaToric 1.0: Continuous-time quantum Monte Carlo for the toric code in a parallel field