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

Area of Science:

• Condensed Matter Physics
• Quantum Information Theory
• Quantum Geometry

Background:

• Bipartite fluctuations of conserved charges offer insights into quantum systems.
• Corner contributions to bipartite fluctuations show universal angle dependence in 2D uniform systems.

Purpose of the Study:

• To establish the direct relationship between corner charge fluctuations and quantum geometry in generic lattice systems.
• To develop a practical method for isolating corner contributions on lattices.
• To demonstrate the use of corner charge fluctuations as a probe of quantum geometry in quantum simulators.

Main Methods:

• Development of a practical scheme to isolate corner contributions to bipartite fluctuations on lattices.
• Analytical proof of the angle dependence in the small-angle limit measuring the integrated quantum metric.
• Introduction of a compact obstructed atomic insulator model for analytical illustration.
• Numerical verification using various Chern insulator models.

Main Results:

• Corner charge fluctuation's angle dependence in the small-angle limit exclusively measures the integrated quantum metric for generic lattice systems.
• Analytical and numerical evidence confirms the link between corner charge fluctuations and quantum geometry.
• Demonstration of corner charge fluctuation's experimental relevance in finite-size quantum simulators.
• Unveiling a connection between quantum geometry and quantum information via corner entanglement entropies for free fermions.

Conclusions:

• Corner charge fluctuations provide a direct and experimentally relevant probe of quantum geometry in lattice systems.
• The study bridges quantum geometry, quantum information, and condensed matter physics through lattice observable measurements.
• Findings have implications for understanding topological phases and designing quantum information processing protocols.