Emergent geometry from entanglement structure

TL;DR

This paper proposes a method to derive emergent geometric structures from the entanglement patterns of quantum many-body states, revealing potential new geometries and insights into entanglement flow.

Contribution

It introduces a generalized adjacency matrix representation of entanglement entropies for all bipartitions, enabling the extraction of emergent geometry from quantum states.

Findings

Representation often exact for various states

Yields a natural entanglement contour

Extends formalism to conformal invariant systems

Abstract

We attempt to reveal the geometry, emerged from the entanglement structure of any general $N$-party pure quantum many-body state by representing entanglement entropies corresponding to all $2^N $ bipartitions of the state by means of a generalized adjacency matrix. We show this representation is often exact and may lead to a geometry very different than suggested by the Hamiltonian. Moreover, in all the cases, it yields a natural entanglement contour, similar to previous proposals. The formalism is extended for conformal invariant systems, and a more insightful interpretation of entanglement is presented as a flow among different parts of the system.