SciPost Submission Page
Electronic bounds in magnetic crystals
by Daniel Passos, Ivo Souza
Submission summary
| Authors (as registered SciPost users): | Daniel Passos · Ivo Souza |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2509.16121v2 (pdf) |
| Date submitted: | Sept. 29, 2025, 5:17 p.m. |
| Submitted by: | Daniel Passos |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
We present a systematic study of bound relations between different electronic properties of magnetic crystals: electron density, effective mass, orbital magnetization, localization length, Chern invariant, and electric susceptibility. All relations are satisfied for a group of low-lying bands, while some remain valid for upper bands. New results include a lower bound on the electric susceptibility of Chern insulators, and an upper bound on the sum-rule part of the orbital magnetization. In addition, bounds involving the Chern invariant are generalized from two dimensions (Chern number) to three (Chern vector). Bound relations are established for metals as well as insulators, and are illustrated for model systems. The manner in which they approach saturation in a model Chern insulator with tunable flat bands is analyzed in terms of the optical absorption spectrum.
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
Current status:
Reports on this Submission
Strengths
2-The currently known bounds are well organized, making the work valuable as a review as well.
Report
I believe the manuscript is suitable for publication in its present form; however, I recommend that the authors address the following questions before final acceptance.
1-How does Eq. (9) guarantee gauge invariance? It may be helpful to add a few explanatory sentences in the manuscript.
Related to this point, while T_p(k) is gauge invariant for p ≥ 0, is it also gauge invariant for p<0? In particular, for p=−1, it is related to the electric susceptibility, so I would expect gauge invariance to hold at least when F_k is the ground-state manifold.
2-Regarding the 3D matrix-invariant inequalities, the magnitude of the Chern vector is bounded by the quantum metric in its direction. However, in cases such as the layered Haldane model discussed in Sec. 6.3.1, where the Chern vector takes the form K=(0,0,K_z), the inequality in Eq. (88) is reduced to the conventional 2D-matrix inequality in Eq. (57). What are the nontrivial situations that arise specifically in three dimensions? For example, do such cases correspond to situations where more than one component of the Chern vector is finite, such as K=(K_x, 0, K_z)?
Recommendation
Ask for minor revision