Emergent geometry from entanglement structure
Abstract
Entanglement entropy representations using generalized adjacency matrices reveal geometric structures in quantum many-body states that differ from Hamiltonian-based geometries and provide insights into entanglement flows in conformal invariant systems.
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.
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