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Bootstrapping frustrated magnets: the fate of the chiral ${\rm O}(N)\times {\rm O}(2)$ universality class
by Marten Reehorst, Slava Rychkov, Benoit Sirois, Balt C. van Rees
Submission summary
| Authors (as registered SciPost users): | Marten Reehorst · Slava Rychkov |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2405.19411v4 (pdf) |
| Date submitted: | 2025-01-07 16:40 |
| Submitted by: | Reehorst, Marten |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We study multiscalar theories with $\text{O}(N) \times \text{O}(2)$ symmetry. These models have a stable fixed point in $d$ dimensions if $N$ is greater than some critical value $N_c(d)$. Previous estimates of this critical value from perturbative and non-perturbative renormalization group methods have produced mutually incompatible results. We use numerical conformal bootstrap methods to constrain $N_c(d)$ for $3 \leq d < 4$. Our results show that $N_c> 3.78$ for $d = 3$. This favors the scenario that the physically relevant models with $N = 2,3$ in $d=3$ do not have a stable fixed point, indicating a first-order transition. Our result exemplifies how conformal windows can be rigorously constrained with modern numerical bootstrap algorithms.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
List of changes
-Replaced "At this point the local minimum turns into a saddle, which we noticed by explicitly computing the Hessian, and the navigator function itself is still negative so we are within the island"
with:
"At this point the local minimum collides with a saddle, leading to the disappearance of both. Precisely at this transition, one Hessian eigenvalue is zero, which we checked by explicitly computing the Hessian. However, the navigator function itself is still negative so we are within the island" (edited) .
-Updated grant acknowledgement according to new guidelines.