2013/06/30 by Yirun Arthur Lee, Guifre Vidal
Physics and Astronomy · #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physreva.88.042318
published as Phys. Rev. A 88, 042318 (2013) · 14 pages, 5 figures (discussion enlarged) -- results closely related to C. Castelnovo, arXiv:1306.4990
arxiv created 2013/06/30 · arxiv updated 2015/06/16
We use the entanglement negativity, a measure of entanglement for mixed states, to probe the structure of entanglement in the ground state of a topologically ordered system. Through analytical calculations of the negativity in the ground state(s) of the toric code model, we explicitly show that the entanglement of a region A and its complement B is the sum of two types of contributions. The first type of contributions consists of boundary entanglement, which we see to be insensitive to tracing out the interior of A and B. It therefore entangles only degrees of freedom in A and B that are close to their common boundary. As it is well-known, each boundary contribution is proportional to the size of the relevant boundary separating A and B and it includes an additive, universal correction. The second contribution appears only when A and B are non-contractible regions (e.g. on a torus) and it consists of long-range entanglement, which we see to be destroyed when tracing out a non-contractible region in the interior of A or B. Only the long-range contribution to the entanglement may depend on the specific ground state under consideration.