Singha Roy, SudiptoSantalla, Silvia N.Sierra, GermánRodríguez Laguna, Javier2024-05-202024-05-202020-05-202469-9969http://doi.org/10.1088/1742-5468/aab67dhttps://hdl.handle.net/20.500.14468/12049We 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.eninfo:eu-repo/semantics/openAccessjournal article