Quantum Geometry and Entanglement in Two-dimensional Insulators: A View from the Corner Charge Fluctuation

• URL: http://arxiv.org/abs/2406.17023v1
• Date: Mon, 24 Jun 2024 18:00:03 GMT
• Title: Quantum Geometry and Entanglement in Two-dimensional Insulators: A View from the Corner Charge Fluctuation
• Authors: Pok Man Tam, Jonah Herzog-Arbeitman, Jiabin Yu,
• Abstract summary: We show that corner charge fluctuation reveals universal information even for generic $textitlattice$ systems of non-interacting electrons. We also highlight a remarkable connection between quantum geometry and quantum information through the lens of corner entanglement entropies.
• Score: 0.5120567378386615
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Measuring bipartite fluctuations of a conserved charge, such as the particle number, within a finite region is a powerful approach to characterizing quantum systems. When the measured region has sharp corners, the bipartite fluctuation receives an additional contribution known to exhibit universal angle-dependence in 2D isotropic and uniform systems. Here we establish that the corner charge fluctuation reveals universal information even for generic $\textit{lattice}$ systems of non-interacting electrons. We first prove that universal angle-dependence can be recovered in the $\textit{small-angle}$ limit for proper partitions of the lattice, from which the integrated Fubini-Study quantum metric can be extracted. A model of a compact obstructed atomic insulator is introduced to illustrate this effect analytically. Numerical verification is presented for various Chern insulator models, demonstrating the experimental relevance of the corner charge fluctuation in a finite-size quantum simulator as a probe of quantum geometry. Last but not least, we highlight a remarkable connection between quantum geometry and quantum information through the lens of corner entanglement entropies.

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