We explore the connection between the area law for entanglement and geometry by representing the entanglement entropies corresponding to all 2 N bipartitions of an N -party pure quantum system by means of a (generalized) adjacency matrix. In the cases where the representation is exact, the elements of that matrix coincide with the mutual information between pairs of sites. In others, it provides a very good approximation, and in all the cases it yields a natural entanglement contour which is similar to previous proposals. Moreover, for one-dimensional conformal invariant systems, the generalized adjacency matrix is given by the two-point correlator of an entanglement current operator. We conjecture how this entanglement current may give rise to a metric entirely built from entanglement.
The registered version of this article, first published in PHYSICAL REVIEW B, is available online at the publisher's website: American Physical Society, https://doi.org/10.1088/1742-5468/aab67d
