Realizing the entanglement Hamiltonian of a topological quantum Hall system

Quentin Redon, Qi Liu, Jean-Baptiste Bouhiron, Nehal Mittal, Aurélien Fabre, Raphael Lopes and Sylvain Nascimbene ()
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Quentin Redon: ENS-PSL University, Sorbonne Université
Qi Liu: ENS-PSL University, Sorbonne Université
Jean-Baptiste Bouhiron: ENS-PSL University, Sorbonne Université
Nehal Mittal: ENS-PSL University, Sorbonne Université
Aurélien Fabre: ENS-PSL University, Sorbonne Université
Raphael Lopes: ENS-PSL University, Sorbonne Université
Sylvain Nascimbene: ENS-PSL University, Sorbonne Université

Nature Communications, 2024, vol. 15, issue 1, 1-14

Abstract: Abstract Topological quantum many-body systems are characterized by a hidden order encoded in the entanglement between their constituents. While entanglement is often quantified using the entanglement entropy, its full description relies on the entanglement Hamiltonian, which is commonly used to identify complex phases arising in numerical simulations, but whose measurement remains an outstanding challenge. Here, we map entanglement to spectral properties by realizing a physical system whose single-particle dynamics is governed by the entanglement Hamiltonian of a quantum Hall system. We use a synthetic dimension, encoded in the electronic spin of dysprosium atoms, to implement spatially deformed dynamics, as suggested by the Bisognano-Wichmann prediction. The realized Hamiltonian, probed with bosonic atoms with negligible interactions, exhibits a chiral dispersion akin to a topological edge mode, revealing the fundamental link between entanglement and boundary physics. We numerically show that our protocol could be extended to interacting systems in fractional quantum Hall states.

Date: 2024
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DOI: 10.1038/s41467-024-54085-5

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