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arXiv · 1906.05146

Entanglement as geometry and flow

Sudipto Singha Roy·Silvia N. Santalla·Javier Rodríguez-Laguna·Germán Sierra
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Abstract

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 {\em 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 {\em entanglement current} operator. We conjecture how this entanglement current may give rise to a metric entirely built from entanglement.

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Sudipto Singha Roy, Silvia N. Santalla, Javier Rodríguez-Laguna, Germán Sierra. 2020-05-25. Entanglement as geometry and flow. https://doi.org/10.1103/physrevb.101.195134

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