Geometric Entanglement in Topologically Ordered States

Understand

Here we investigate the connection between 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.
• This topological contribution is also present in the case of single-spin blocks in most cases, and constitutes an alternative characterisation of topological order for these quantum states based on a multipartite entanglement measure.