Geometric Entanglement in Topologically Ordered States: Theory and Numerics

Geometric Entanglement in Topologically Ordered States: Theory and Numerics

Seminar author:Roman Orus

Event date and time:02/26/2014 03:00:pm

Event location:IFAE seminar room

Event contact:

Here we present the connection between 2d topological order and the geometric entanglement, as measured by the logarithm of the overlap between a given state and its closest product state of blocks. We do this for a variety of topologically-ordered systems such as the toric code, double semion, color code, and quantum double models. As happens for the entanglement entropy, we find that for sufficiently large block sizes the geometric entanglement is, up to possible sub-leading corrections, the sum of two contributions: a bulk contribution obeying a boundary law times the number of blocks, and a contribution quantifying the underlying pattern of long-range entanglement of the topologically-ordered state. Moreover, we present a very efficient numerical method based on tensor networks to compute this topological contribution for a PEPS with a string tension. Several examples of topological phase transitions are discussed in this context. Our results also indicate that entanglement loss along renormalization group flows is not necessarily present in 2d topological phases, in accordance with recent results by other authors.