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  9. Mathematical Aspects Of Quantum And Conformal Field Theory, Quantum Gravity And String Theory
  11. Instantaneous Response And Quantum Geometry Of Insulators

Instantaneous response and quantum geometry of insulators

Nishchhal Verma1, Raquel Queiroz1,2

  • 1Department of Physics, Columbia University, New York, NY 10027.

Proceedings of the National Academy of Sciences of the United States of America
|December 4, 2025

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View abstract on PubMed

Summary
This summary is machine-generated.

We introduce the time-dependent Quantum Geometric Tensor (tQGT) to analyze insulators. This tool captures electron motion and electronic conductivity, providing a framework for calculating material properties like optical mass and dielectric constant.

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.
Keywords:
flat bandsquantum geometrysum rulestopological insulators

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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.