SciPost Physics

SciPost Phys. 13, 014 (2022) · published 8 August 2022

• doi: 10.21468/SciPostPhys.13.2.014
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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.

• Bertucci et al., Analytic bootstrap of mixed correlators in the O(n) CFT
  J. High Energ. Phys. 2022, 104 (2022) [Crossref]
• Karthik et al., Scaling dimension of the 4π -flux monopole operator in four-flavor three-dimensional QED using lattice simulation
  Phys. Rev. D 109, 034507 (2024) [Crossref]
• Lanzetta et al., Bootstrapping Lieb-Schultz-Mattis anomalies
  Phys. Rev. B 107, 205137 (2023) [Crossref]
• Ye et al., Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality
  SciPost Phys. 13, 066 (2022) [Crossref]
• Henriksson, The critical O(N) CFT: Methods and conformal data
  Physics Reports 1002, 1 (2023) [Crossref]
• Luo et al., Twisted bilayer U(1) Dirac spin liquids
  Phys. Rev. B 106, 144437 (2022) [Crossref]
• Chester et al., Bootstrapping Deconfined Quantum Tricriticality
  Phys. Rev. Lett. 132, 111601 (2024) [Crossref]
• Di Pietro et al., Vacuum stability, fixed points, and phases of QED3 at large Nf
  Phys. Rev. D 108, L061902 (2023) [Crossref]
• Song et al., Emergent QED3 from half-filled flat Chern bands
  Phys. Rev. B 108, 205123 (2023) [Crossref]
• Budaraju et al., Piercing the Dirac spin liquid: From a single monopole to chiral states
  Phys. Rev. B 108, L201116 (2023) [Crossref]
• Nambiar et al., Monopole Josephson effects in a Dirac spin liquid
  Phys. Rev. Research 5, 013169 (2023) [Crossref]
• He et al., Non-Abelian currents bootstrap
  J. High Energ. Phys. 2024, 175 (2024) [Crossref]