Instantaneous response and quantum geometry of insulators

Area of Science:

• Condensed matter physics
• Quantum mechanics
• Materials science

Background:

• Insulators possess unique electronic properties governed by their quantum geometry.
• Linear response theory is crucial for understanding material responses to external fields.

Purpose of the Study:

• Introduce the time-dependent Quantum Geometric Tensor (tQGT) as a novel tool.
• Provide a systematic framework for calculating instantaneous electronic responses in insulators.
• Explore the generation of quantum geometry in periodic systems.

Main Methods:

• Formulation of the time-dependent Quantum Geometric Tensor (tQGT).
• Application of tQGT within linear response theory.
• Analysis of electronic conductivity sum rules.
• Investigation of lattice interference effects in periodic systems.

Main Results:

• tQGT captures the zero-point motion of bound electrons.
• tQGT serves as a generating function for generalized electronic conductivity sum rules.
• Consistent approximations for optical mass, orbital angular momentum, and dielectric constant are achieved.
• Lattice interference can generate quantum geometry, leading to spectral weight transfer and flat bands.

Conclusions:

• The tQGT offers a comprehensive geometric characterization of insulators.
• This framework enables accurate computation of instantaneous electronic properties.
• Geometrically frustrated flat bands present novel avenues for spectral manipulation.