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Statut |
Confirmé |
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Série |
FORUM-ENS |
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Domaines |
cond-mat.stat-mech |
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Date |
Mercredi 30 Septembre 2020 |
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Heure |
12:00 |
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Institut |
LPENS |
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Salle |
https://www.gotomeet.me/forumphystat |
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Nom de l'orateur |
Estienne |
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Prenom de l'orateur |
Benoit |
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Addresse email de l'orateur |
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Institution de l'orateur |
Laboratoire de Physique Théorique et Hautes Énergies Sorbonne Université |
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Titre |
Bulk & Boundary Entanglement Entropy in the Quantum Hall Effect: Exact Results |
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Résumé |
Ideas coming from quantum information theory have provided invaluable insights
and powerful tools for quantum many-body systems. One of the most basic tools
in the arsenal of quantum information theory is entanglement entropy. A
particularly striking phenomenon is the area law of entanglement entropy, which
has been widely discussed in recent years in condensed matter and quantum field
theories. Typically, one considers a many-particle state and a geometric
partition of the space in two sub-regions. The von Neumann entropy of the
reduced state of a sub-region measures the degree of entanglement between the
two regions. The area law states that the leading semiclassical asymptotics of
the entanglement entropy is proportional to the volume of the boundary of the
sub-region.
I will start with an introduction to quantum entanglement, entanglement
entropy, and their applications in condensed matter. I will present some exact
results obtained with L. Charles in the context of the (integer) quantum Hall
effect regarding both the entanglement entropy and full counting statistics,
namely proof of the Area law (arXiv:1803.03149) in the bulk of the quantum Hall
droplet. I will conclude with some recent results obtained with J.M. Stephan
(arXiv:1911.10125) showing how the entanglement entropy is capable of detecting
the critical one-dimensional modes at the boundary of the quantum Hall droplet. |
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Numéro de preprint arXiv |
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