2013/06/30 by Claudio Castelnovo · 6 citations
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Discrete mathematics #Graph #Mathematics #Negativity effect #Physics #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum and electron transport phenomena #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Statistical physics #Topological entropy #Topological entropy in physics #Topological order #Topological quantum number #Topology (electrical circuits) #Toric code #Vertex (graph theory) #Von Neumann architecture #Von Neumann entropy #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physreva.88.042319
published as Physical Review A 88, 042319 (2013) · (5 pages, 1 figure; a mistake in v1 has been corrected in v2; typos and references fixed in v3)
arxiv created 2013/09/27 · openalex publication_date 2013/10/16 · arxiv updated 2014/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper we study the behavior of the entanglement measure dubbed negativity in the context of the toric code model. Using a replica method introduced recently by Calabrese, Cardy, and Tonni [Phys. Rev. Lett. 109, 130502 (2012)], we obtain an exact expression which illustrates how the nonlocal correlations present in a topologically ordered state reflect in the behavior of the negativity of the system. We find that the negativity has a leading area-law contribution if the subsystems are in direct contact with one another (as expected in a zero-range correlated model). We also find a topological contribution directly related to the topological entropy, provided that the partitions are topologically nontrivial in both directions on a torus. We further confirm by explicit calculation that the negativity captures only quantum contributions to the entanglement. Indeed, we show that the negativity vanishes identically for the classical topologically ordered eight-vertex model, which on the contrary exhibits a finite von Neumann entropy, inclusive of topological correction.