Quantum simulator of extended bipartite Hubbard model with broken sublattice symmetry: magnetism, correlations, and phase transitions
Bibliographic record
Abstract
We describe here a quantum simulator of extended bipartite Hubbard model with broken sublattice symmetry. The simulator consists of a structured lateral gate confining two dimensional electrons in a quantum well into artificial minima arranged in a hexagonal lattice. The sublattice symmetry breaking is generated by forming an artificial triangular graphene quantum dot (ATGQD) with zigzag edges. The resulting extended Hubbard model generates tunable ratio of tunneling strength to electron-electron interactions and of sublattice symmetry with control over shape. The validity of the simulator is confirmed for small systems using mean-field and exact diagonalization many-body approaches which show that the ground state changes from a metallic to an antiferromagnetic (AF) phase by varying the distance between sites or depth of the confining potential. The one-electron spectrum of these triangular dots contains a macroscopically degenerate shell at the Fermi level. The shell persists at the mean-field level for weak interactions (metallic phase) but disappears for strong interactions, in the AF phase. We determine the effects of electron-electron interactions on the ground state, the total spin, and the excitation spectrum as a function of filling of the ATGQD. We find that the half-filled charge neutral shell leads to a partially spin polarized state in both metallic and AF regimes in accordance with Liebs theorem. In both regimes a relatively large gap separates the spin polarized ground state to the first excited many-body state at half filling of the degenerate shell. By adding or removing an electron, this gap drops dramatically, and alternate total spin states emerge with energies nearly degenerate to a spin polarized ground state.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".