AI Article Synopsis
- The text discusses a universal way to understand quantum entanglement in the ground state of a two-dimensional system with topological order and a mass gap.
- It focuses on a disk shape area where the boundary is significantly larger than the correlation length, and calculates a density operator for the area inside the disk after ignoring the outside.
- The key finding is that the von Neumann entropy, which quantifies the entanglement, has a specific formula involving a constant (gamma) that reflects an overall feature of the ground state's entanglement structure, derived using topological quantum field theory.
Article Abstract
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.
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| http://dx.doi.org/10.1103/PhysRevLett.96.110404 | DOI Listing |
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