Topological Entanglement Entropy

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…

• NS
  National Science Foundation

  Award: 0456720
• UD
  U.S. Department of Energy

  Award: DE-FG03-92-ER40701
• CI
  California Institute of Technology
• DA
  Deutscher Akademischer Austauschdienst
• MU
  Multidisciplinary University Research Initiative
• AR
  Army Research Office

  Award: W911NF