# Conformal bootstrap bounds for the $U(1)$ Dirac spin liquid and $N=7$ Stiefel liquid

### Submission summary

 As Contributors: Yin-Chen He · Junchen Rong Arxiv Link: https://arxiv.org/abs/2107.14637v3 (pdf) Date accepted: 2022-06-21 Date submitted: 2022-05-17 05:45 Submitted by: He, Yin-Chen Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory High-Energy Physics - Theory Approaches: Theoretical, Computational

### Abstract

We apply the conformal bootstrap technique to study the $U(1)$ Dirac spin liquid (i.e. $N_f=4$ QED$_3$) and the newly proposed $N=7$ Stiefel liquid (i.e. a conjectured 3d non-Lagrangian CFT without supersymmetry). For the $N_f=4$ QED$_3$, we focus on the monopole operator and ($SU(4)$ adjoint) fermion bilinear operator. We bootstrap their single correlators as well as the mixed correlators between them. We first discuss the bootstrap kinks from single correlators. Some exponents of these bootstrap kinks are close to the expected values of QED$_3$, but we provide clear evidence that they should not be identified as the QED$_3$. By requiring the critical phase to be stable on the triangular and the kagome lattice, we obtain rigorous numerical bounds for the $U(1)$ Dirac spin liquid and the Stiefel liquid. For the triangular and kagome Dirac spin liquid, the rigorous lower bounds of the monopole operator's scaling dimension are $1.046$ and $1.105$, respectively. These bounds are consistent with the latest Monte Carlo results.

Published as SciPost Phys. 13, 014 (2022)

### List of changes

Besides the changes of gramma mistakes and typos, we added clarifications regarding our definition of non-Lagrangian CFT in the introduction.

### Submission & Refereeing History

#### Published as SciPost Phys. 13, 014 (2022)

Resubmission 2107.14637v3 on 17 May 2022
Submission 2107.14637v2 on 18 November 2021

## Reports on this Submission

### Report

I am happy to recommend this paper to publication in the present form.

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### Report

Due to the recent changes, I think this paper can now be published. It is notable that the authors list at least four combinations of correlators that were studied but not used in any figures. This could help save time in one of the ongoing QED3 searches.

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -