2005/10/31 by Alexei Kitaev, John Preskill · 5 citations
Mathematics · Physics and Astronomy · #Entropy (arrow of time) #Ground state #Mass gap #Mathematical physics #Mathematics #Operator (biology) #Physics #Quantum #Quantum and electron transport phenomena #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Topological Materials and Phenomena #Topological entropy in physics #Topological quantum number #Topology (electrical circuits) #Von Neumann entropy #cond-mat.str-el #hep-th #quant-ph
paper · pdf · doi:10.1103/physrevlett.96.110404
published as Phys.Rev.Lett. 96 (2006) 110404 · 4 pages, 3 eps figures. v2: reference added
arxiv created 2006/01/23 · openalex publication_date 2006/03/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We formulate a universal characterization of the many-particle quantum entanglement in the ground state of a topologically ordered two-dimensional medium with a mass gap. We consider a disk in the plane, with a smooth boundary of length L, large compared to the correlation length. In the ground state, by tracing out all degrees of freedom in the exterior of the disk, we obtain a marginal density operator rho for the degrees of freedom in the interior. The von Neumann entropy of rho, a measure of the entanglement of the interior and exterior variables, has the form S(rho) = alphaL - gamma + ..., where the ellipsis represents terms that vanish in the limit L --> infinity. We show that - gamma is a universal constant characterizing a global feature of the entanglement in the ground state. Using topological quantum field theory methods, we derive a formula for gamma in terms of properties of the superselection sectors of the medium.