Quantum weight
Abstract: We introduce the concept of quantum weight as a fundamental property of insulating states of matter that is encoded in the ground-state static structure and measures quantum fluctuation in electrons' center of mass. We find a sum rule that directly relates quantum weight -- a ground state property -- with the negative-first moment of the optical conductivity above the gap frequency. Building on this connection to optical absorption, we derive both an upper bound and a lower bound on quantum weight in terms of electron density, dielectric constant, and energy gap. Therefore, quantum weight constitutes a key material parameter that can be experimentally determined from X-ray scattering.
- R. Kubo, Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems, Journal of the Physical Society of Japan 12, 570 (1957).
- Y. Onishi and L. Fu, Universal relation between energy gap and dielectric constant (2024), arXiv:2401.04180 [cond-mat].
- Y. Onishi and L. Fu, Fundamental bound on topological gap (2023), arXiv:2306.00078 [cond-mat].
- I. Souza, T. Wilkens, and R. M. Martin, Polarization and localization in insulators: Generating function approach, Physical Review B 62, 1666 (2000), publisher: American Physical Society.
- H. B. Callen and T. A. Welton, Irreversibility and Generalized Noise, Physical Review 83, 34 (1951), publisher: American Physical Society.
- R. Kubo, M. Yokota, and S. Nakajima, Statistical-Mechanical Theory of Irreversible Processes. II. Response to Thermal Disturbance, Journal of the Physical Society of Japan 12, 1203 (1957).
- R. Resta, Polarization Fluctuations in Insulators and Metals: New and Old Theories Merge, Physical Review Letters 96, 137601 (2006), publisher: American Physical Society.
- We note that the static structure factor for metallic systems at small 𝒒𝒒{\bf\it q}bold_italic_q is dominated by |q|𝑞\absolutevalue{q}| start_ARG italic_q end_ARG |-linear term, in contrast to insulators where the leading order term is quadratic.
- O. Madelung, Semiconductors: data handbook (Springer Science & Business Media, 2004).
- S. Peotta and P. Törmä, Superfluidity in topologically nontrivial flat bands, Nature Communications 6, 8944 (2015), number: 1 Publisher: Nature Publishing Group.
- S. Kivelson, Wannier functions in one-dimensional disordered systems: Application to fractionally charged solitons, Physical Review B 26, 4269 (1982), publisher: American Physical Society.
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