Transition from a Dirac spin liquid to an antiferromagnet: Monopoles in a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>QED</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math>-Gross-Neveu theory
Bibliographic record
Abstract
We study the quantum phase transition from a Dirac spin liquid to an antiferromagnet driven by condensing monopoles with spin quantum numbers. We describe the transition in field theory by tuning a fermion interaction to condense a spin-Hall mass, which in turn allows the appropriate monopole operators to proliferate and confine the fermions. We compute various critical exponents at the quantum critical point (QCP), including the scaling dimensions of monopole operators by using the state-operator correspondence of conformal field theory. We find that the degeneracy of monopoles in ${\mathrm{QED}}_{3}$ is lifted and yields a nontrivial monopole hierarchy at the QCP. In particular, the lowest monopole dimension is found to be smaller than that of ${\mathrm{QED}}_{3}$ using a large-${N}_{f}$ expansion, where $2{N}_{f}$ is the number of fermion flavors. For the minimal magnetic charge, this dimension is $0.39{N}_{f}$ at leading order. We also study the QCP between Dirac and chiral spin liquids, which allows us to test a conjectured duality to a bosonic ${\mathrm{CP}}^{1}$ theory. Finally, we discuss the implications of our results for quantum magnets on the kagome lattice.
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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 | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".