Quantum weight

Quantum weight

June 12, 2024 | Yugo Onishi and Liang Fu
The concept of quantum weight is introduced as a fundamental property of quantum many-body systems, encoded in the ground-state static structure factor and characterizing density fluctuations at long wavelengths. It is related to the inverse dielectric function, which describes electron energy loss spectra. Using this relationship, upper and lower bounds on quantum weight are derived for real materials in terms of electron density, static dielectric constant, and plasmon energy. For systems with short-range interactions or Coulomb systems in reduced dimensions, a sum rule relating quantum weight to optical conductivity is established, highlighting its connection to the quantum geometry of many-body ground states. The quantum weight is shown to be equal to the many-body quantum metric in systems with short-range interactions or reduced dimensions, but differs in 3D Coulomb systems due to Coulomb screening. The quantum weight can be experimentally determined and is a key material parameter. The work also discusses the connection between quantum weight and quantum metric, showing that they are equal in certain systems. The results are illustrated with examples such as diamond and cubic boron nitride, where the quantum weight is bounded within a narrow range. The study provides a framework for understanding the relationship between quantum weight, optical conductivity, and many-body quantum metric in various materials.The concept of quantum weight is introduced as a fundamental property of quantum many-body systems, encoded in the ground-state static structure factor and characterizing density fluctuations at long wavelengths. It is related to the inverse dielectric function, which describes electron energy loss spectra. Using this relationship, upper and lower bounds on quantum weight are derived for real materials in terms of electron density, static dielectric constant, and plasmon energy. For systems with short-range interactions or Coulomb systems in reduced dimensions, a sum rule relating quantum weight to optical conductivity is established, highlighting its connection to the quantum geometry of many-body ground states. The quantum weight is shown to be equal to the many-body quantum metric in systems with short-range interactions or reduced dimensions, but differs in 3D Coulomb systems due to Coulomb screening. The quantum weight can be experimentally determined and is a key material parameter. The work also discusses the connection between quantum weight and quantum metric, showing that they are equal in certain systems. The results are illustrated with examples such as diamond and cubic boron nitride, where the quantum weight is bounded within a narrow range. The study provides a framework for understanding the relationship between quantum weight, optical conductivity, and many-body quantum metric in various materials.
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