Competing phases and critical behaviour in three coupled spinless Luttinger liquids
Bibliographic record
Abstract
We study electronic phase competition in a strongly correlated system of three coupled spinless Luttinger liquids—one of the simplest models where topologically nontrivial chiral orders may be realized. We study the problem as a coupled sine-Gordon model, using a perturbative renormalization group (RG) approach. In contrast with counterparts with fewer fermionic species, here the scaling procedure generates off-diagonal contributions to the phase stiffness matrix, which require both rescaling as well as large rotations of the bosonic fields. These rotations, generally non-abelian in nature, introduce a coupling between different interaction channels even at the tree-level order in the coupling constant scaling equations. We study competing phases in this system, taking into account the aforementioned rotations, and determine its critical behaviour in a variety of interaction parameter regimes where perturbative RG is possible. The phase boundaries are found to be of the Berezinskii–Kosterlitz–Thouless type, and we specify the parameter regimes where symmetry breaking between the three flavours of bosonic fields, orders involving different flavours, and chiral orders may be observed. Our approach and findings may be relevant for understanding phases and transitions at high magnetic fields in semimetals such as bismuth featuring three Fermi pockets.
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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 | 0.001 |
| 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".