Redon Quentin, Liu Qi, Bouhiron Jean-Baptiste, Mittal Nehal, Fabre Aurélien, Lopes Raphael, Nascimbene Sylvain
Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, Paris, France.
Nat Commun. 2024 Nov 21;15(1):10086. doi: 10.1038/s41467-024-54085-5.
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.
拓扑量子多体系统的特征是其组成部分之间纠缠中编码的隐藏序。虽然纠缠通常使用纠缠熵来量化，但其完整描述依赖于纠缠哈密顿量，该量通常用于识别数值模拟中出现的复杂相，但其测量仍然是一个突出的挑战。在这里，我们通过实现一个物理系统，将纠缠映射到光谱特性，该物理系统的单粒子动力学由量子霍尔系统的纠缠哈密顿量控制。我们使用在镝原子的电子自旋中编码的合成维度来实现空间变形动力学，正如比索尼亚诺 - 维希曼预测所建议的那样。用相互作用可忽略不计的玻色原子探测所实现的哈密顿量，表现出类似于拓扑边缘模式的手性色散，揭示了纠缠与边界物理之间的基本联系。我们通过数值计算表明，我们的方案可以扩展到分数量子霍尔态的相互作用系统。
