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arXiv · 2308.13706

Quasilocal entanglement across the Mott-Hubbard transition

Gabriele Bellomia·Carlos Mejuto-Zaera·Massimo Capone·Adriano Amaricci
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Abstract

The possibility to directly measure, in a cold-atom quantum simulator, the von Neumann entropy and mutual information between a site and its environment opens new perspectives on the characterization of the Mott-Hubbard metal-insulator transition, in the framework of quantum information theory. In this work we provide an alternative view of the Mott transition in the two-dimensional Hubbard model in terms of rigorous quasilocal measures of entanglement and correlation between two spatially separated electronic orbitals, with no contribution from their environment. A space-resolved analysis of cluster dynamical mean-field theory results elucidates the prominent role of the nearest-neighbor entanglement in probing Mott localization: both its lower and upper bounds sharply increase at the metal-insulator transition. The two-site entanglement beyond nearest neighbors is shown to be quickly damped as the inter-site distance is increased. These results ultimately resolve a conundrum of previous analyses based on the single-site von Neumann entropy, which has been found to monotonically decrease when the interaction is increased. The quasilocal two-site entanglement recovers instead the distinctive character of Mott insulators as strongly correlated quantum states, demonstrating its central role in the $2d$ Hubbard model.

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Gabriele Bellomia, Carlos Mejuto-Zaera, Massimo Capone, Adriano Amaricci. 2024-03-08. Quasilocal entanglement across the Mott-Hubbard transition. https://doi.org/10.1103/physrevb.109.115104

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