SciPost Submission Page
Optical bounds on many-electron localization
by Ivo Souza, Richard M. Martin and Massimiliano Stengel
Submission summary
| Authors (as registered SciPost users): | Ivo Souza |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202407_00046v2 (pdf) |
| Date accepted: | 2025-04-02 |
| Date submitted: | 2025-02-28 17:08 |
| Submitted by: | Souza, Ivo |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
We establish rigorous inequalities between different electronic properties linked to optical sum rules, and organize them into weak and strong bounds on three characteristic properties of insulators: electron localization length ℓ (the quantum fluctuations in polarization), electric susceptibility χ, and optical gap EG. All-electron and valence-only versions of the bounds are given, and the latter are found to be more informative. The bounds on~ℓ are particularly interesting, as they provide reasonably tight estimates for an ellusive ground-state property --~the average localization length of valence electrons~-- from tabulated experimental data: electron density, high-frequency dielectric constant, and optical gap. The localization lengths estimated in this way for several materials follow simple chemical trends, especially for the alkali halides. We also illustrate our findings via analytically solvable harmonic oscillator models, which reveal an intriguing connection to the physics of long-ranged van der Waals forces.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
We would like to thank both referees for their thoughtful and constructive remarks on our manuscript. As requested, we have made minor changes in response to their comments and suggestions. With the goal of further improving the text, we made a few additional changes at various places, and corrected some typos.
List of changes
Changes in response to the comments of the referees:
* We have rephrased the sentence below Eq. (11):
"These average inverse excitation energies weighted by the transition
strength [18] will be denoted as (inverse) 'average gaps.'"
* A sentence was added below Eq. (25):
"Interestingly, both bounds can be improved by means of correction
terms involving positive moments of the absorption spectrum [18]."
* A sentence was added in the Conclusions:
"The extension to low-symmetry crystals with anisotropic localization
and susceptibility tensors is also straightforward."
Additional changes not directly motivated by the referee reports:
* The notation for the localization tensor in Eqs. (4-7) has changed,
and the meaning of Eq. (5) has also changed slightly.
* Equation (7) has been corrected. The longitudinal localization
length squared was previously written as a Cartesian tensor, when it
is in fact a direction-dependent scalar.
* The caption of Table 1 was shortened.
* At the end of the paragraph below Eq. (10), a discussion was added
on the application of optical sum rules to characterize F centers in
alkali halide crystals, with a new reference [24]. References [22,23]
were also added in the same paragraph, in connection with atomic sum
rules.
* The paragraph about Chern insulators at the end of Sec. 3 was
shortened slightly, by removing a sentence about time-odd sum rules
and inequalities that fall outside the scope of the present work.
* Three footnotes were removed.
* Other minor edits were made to improve the clarity of the text.
Current status:
Editorial decision:
For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)