Emergent <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>U</mml:mi><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math> symmetries in gapless fermionic superfluids and superconductors
Bibliographic record
Abstract
A superfluid spontaneously breaks the usual $U(1)$ symmetry because of condensation. In this article, we illustrate six linearly independent families of emergent $U(1)$ symmetries that naturally appear in infrared limits in a broad class of generic gapless topological superfluids (that either belong to a stable phase or are quantum critical). In gapless states we have considered, emergent $U(1)$ symmetry groups are embedded in a $Spin(4)=SU(2)\ensuremath{\bigotimes}SU(2)$ group that double covers (and algebraically is isomorphic to) an $SO(4)$ group. All $U(1)$ charges associated with symmetries are further invariant under an $SU(2)$ spin group or an equivalent of it but always break preexisting higher space-time Lorentz symmetry of the $SO(3,1)$ group. Emergent $U(1)$ symmetries can be further spontaneously broken only if interactions are strong enough and resultant strong-coupling states become fully gapped. However, if states remain gapless, emergent $U(1)$ symmetries are always present, despite that these states may exhibit much lower space-time symmetries compared to their weakly interacting gapless Lorentz symmetric counterparts. In the limit of our interests, we have identified all possible gapless real fermions with or without Lorentz symmetries and find that they all display emergent $U(1)$ symmetries in the infrared limit. We argue emergent $U(1)$ symmetries are intrinsic in a broad class of interacting gapless superfluid or superconducting states and are typically well defined in high dimensions where there are infrared stable fixed points dictating emergent properties.
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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 | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
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".