Related papers: Corner Charge Fluctuation as an Observable for Quantum Geometry and Entanglement in Two-dimensional Insulators

Corner Charge Fluctuation as an Observable for Quantum Geometry and Entanglement in Two-dimensional Insulators

URL: http://arxiv.org/abs/2406.17023v3
Date: Tue, 17 Sep 2024 02:34:10 GMT
Title: Corner Charge Fluctuation as an Observable for Quantum Geometry and Entanglement in Two-dimensional Insulators
Authors: Pok Man Tam, Jonah Herzog-Arbeitman, Jiabin Yu,
Abstract summary: We show that for generic lattice systems of interacting particles, the corner charge fluctuation is directly related to quantum geometry. A model of a compact obstructed atomic insulator is introduced to illustrate this effect analytically. numerical verification for various Chern insulator models further demonstrate the experimental relevance of the corner charge fluctuation in a finite-size quantum simulator.
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, is a powerful approach to understanding quantum systems. When the measured region has sharp corners, the bipartite fluctuation receives an additional contribution known to exhibit a universal angle-dependence in 2D isotropic and uniform systems. Here we establish that, for generic lattice systems of interacting particles, the corner charge fluctuation is directly related to quantum geometry. We first provide a practical scheme to isolate the corner contribution on lattices, and analytically prove that its angle-dependence in the small-angle limit measures exclusively the integrated quantum metric. A model of a compact obstructed atomic insulator is introduced to illustrate this effect analytically, while numerical verification for various Chern insulator models further demonstrate the experimental relevance of the corner charge fluctuation in a finite-size quantum simulator as a probe of quantum geometry. Last but not least, for free fermions, we unveil an intimate connection between quantum geometry and quantum information through the lens of corner entanglement entropies.

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