Surface topological quantum criticality: Conformal manifolds and discrete strong-coupling fixed points
Bibliographic record
Abstract
In this article, we study quantum critical phenomena in surfaces of symmetry-protected topological matter, i.e., surface topological quantum criticality. A generic phase boundary of gapless surfaces in a symmetry-protected state shall be a codimension one manifold in an interaction parameter space of dimension ${D}_{p}$ (where $p$ refers to the parameter space) where the value of ${D}_{p}$ further depends on bulk topologies. In the context of fermionic topological insulators that we focus on, ${D}_{p}$ depends on the number of half-Dirac cones $\mathcal{N}$. We construct such manifolds explicitly for a few interaction parameter spaces with various ${D}_{p}$ values. Most importantly, we further illustrate that in cases with ${D}_{p}=3$ and 6, there are submanifolds of fixed points that dictate the universalities of surface topological quantum criticality. These infrared stable manifolds are associated with emergent symmetries in the renormalization-group-equation flow naturally appearing in the loop expansion. Unlike in the usual order-disorder quantum critical phenomena, typically governed by an isolated Wilson-Fisher fixed point, we find in the one-loop approximation surface topological quantum criticalities are naturally captured by conformal manifolds where the number of marginal operators uniquely determines their codimensions. Isolated strong-coupling fixed points also appear, usually as the endpoints in the phase boundary of surface topological quantum phases. However, their extreme infrared instabilities along multiple directions suggest that they shall be related to multicritical surface topological quantum critical phenomena rather than generic surface topological quantum criticality. We also discuss and classify higher-loop symmetry-breaking effects, which can either distort the conformal manifolds or further break the conformal manifolds down to a few distinct fixed points.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.003 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".