Optical conductivity of a metal-insulator transition for the Anderson-Hubbard model in three dimensions away from half filling
Bibliographic record
Abstract
The Anderson-Hubbard model is considered to be the least complicated model using lattice fermions with which one can hope to study the physics of transition-metal oxides with spatial disorder. We have completed a numerical investigation of this model for three-dimensional simple-cubic lattices using a real-space self-consistent Hartree-Fock decoupling approximation for the Hubbard interaction. In this formulation we treat the spatial disorder exactly and therefore we account for effects arising from localization physics. We have examined the model for electronic densities well away from 1/2 filling thereby avoiding the physics of a Mott insulator. Several recent studies have made clear that the combined effects of electronic interactions and spatial disorder can give rise to a suppression of the electronic density of states and a subsequent metal-insulator transition can occur. We supplement such studies by calculating the ac conductivity for such systems. Our numerical results show that weak interactions enhance the density of states at the Fermi level and the low-frequency conductivity, there are no local magnetic moments, and the ac conductivity is Drude like. However, with a large enough disorder strength and larger interactions the density of states at the Fermi level and the low-frequency conductivity are both suppressed, the conductivity becomes non-Drude like, and these phenomena are accompanied by the presence of local magnetic moments. The low-frequency conductivity changes from a $\ensuremath{\sigma}\ensuremath{-}{\ensuremath{\sigma}}_{\text{dc}}\ensuremath{\sim}{\ensuremath{\omega}}^{1/2}$ behavior in the metallic phase, to a $\ensuremath{\sigma}\ensuremath{\sim}{\ensuremath{\omega}}^{2}$ behavior in the nonmetallic regime. For intermediate disorder at 1/4 electronic filling, a metal-to-insulator transition is predicted to take place at a critical $U/B\ensuremath{\approx}0.75$ ($U$ being the Hubbard interaction strength and $B$ the electronic band width). Our numerical results show that the formation of magnetic moments is essential to the suppression of the density of states at the Fermi level and therefore essential to the metal-insulator transition. At weaker disorder a small lessening of the density of states at the Fermi level occurs but screening suppresses the spatial disorder and with increasing interactions no metal-insulator transition is found.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".