Topological Geometric Entanglement

TL;DR

This paper explores the relationship between topological order and geometric entanglement in the toric code model, revealing universal and non-universal contributions to entanglement scaling.

Contribution

It establishes a connection between topological order and geometric entanglement, identifying universal contributions related to long-range entanglement patterns.

Findings

Geometric entanglement scales with block size and topology.

Universal contribution quantifies topological long-range entanglement.

Bulk contribution obeys a boundary law.

Abstract

Here we show 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, for the topological universality class of the toric code model. As happens for the entanglement entropy, we find that for large block sizes the geometric entanglement is, up to possible subleading corrections, the sum of two contributions: a non-universal bulk contribution obeying a boundary law times the number of blocks, and a universal contribution quantifying the underlying pattern of long-range entanglement of a topologically-ordered state.