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

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.

14 pages plus refs, 3 figures. Close to the published version

References in corpus (15)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Properties of an algebraic spin liquid on the kagome lattice
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Algebraic spin liquid as the mother of many competing orders
• N=1 Deformations and RG Flows of N=2 SCFTs
• On the Phase Structure of Many-Flavor QED${}_3$
• Chiral symmetry breaking in ${\mathrm{QED}}_3$ in presence of irrelevant interactions: a renormalization group study
• The Renormalization Group Studies on Four Fermion Interaction Instabilities on Algebraic Spin Liquids
• Trisecting non-Lagrangian theories
• Exploring $SU(N)$ adjoint correlators in $3d$
• Theory of Dirac spin liquids on spin-$S$ triangular lattice: possible application to $\alpha$-CrOOH(D)

Cited by in corpus (15)

• The critical O(N) CFT: Methods and conformal data
• Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality
• New Developments in the Numerical Conformal Bootstrap
• Quantum Electrodynamics in 2+1 Dimensions as the Organizing Principle of a Triangular Lattice Antiferromagnet
• Spin-Peierls instability of the U(1) Dirac spin liquid
• Bootstrapping Lieb-Schultz-Mattis anomalies
• Monopole Josephson Effects in a Dirac Spin Liquid
• Twisted bilayer U(1) Dirac spin liquids
• Piercing the Dirac spin liquid: From a single monopole to chiral states
• Dirac spin liquid as an "unnecessary" quantum critical point on square lattice antiferromagnets
• Spin-Peierls instability of deconfined quantum critical points
• Unnecessary quantum criticality in $SU(3)$ kagome magnets
• Stability of algebraic spin liquids coupled to quantum phonons
• When Wannier centers jump: Critical points between atomic insulating phases
• Conformal Bootstrap with Duality-Inspired Fusion Rule