Critical behavior of QED${}_3$--Gross-Neveu-Yukawa Theory in an Arbitrary Gauge

Abstract

The chiral QED${}_3$--Gross-Neveu-Yukawa (QED${}_3$-GNY) theory is a $2+1$-dimensional U(1) gauge theory with $N_f$ flavors of four-component Dirac fermions coupled to a scalar field. For $N_f=1$, the specific chiral Ising QED${}_3$-GNY model has recently been conjectured to be dual to the deconfined quantum critical point that describes Neel--valence-bond-solid transition of frustrated quantum magnets on square lattice. We study the universal critical behaviors of the chiral QED${}_3$-GNY model in $d=4-\epsilon$ dimensions for an arbitrary $N_f$ . We calculate the boson anomalous dimensions, inverse correlation length exponent, as well as the scaling dimensions of nonsinglet fermion bilinear in the chiral QED${}_3$-GNY model. The Pad$\acute{e}$ estimates for the exponents are obtained in the chiral Ising-, XY- and Heisenberg-QED${}_3$-GNY universality class respectively. We also establish the general condition of the supersymmetric criticality for the ungauged QED${}_3$-GNY model. For the conjectured duality between chiral QED${}_3$-GNY critical point and deconfined quantum critical point, we find the inverse correlation length exponent has a lower boundary ${\nu }^{-1}>0.75$, beyond which the Ising-QED${}_3$-GNY--$\mathbb{C}$P${}^1$ duality may hold.

15 pages,5 figures

References in corpus (16)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Electron fractionalization in two-dimensional graphenelike structures
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Algebraic spin liquid as the mother of many competing orders
• Scaling in the Fan of an Unconventional Quantum Critical Point
• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Emergence of supersymmetry at a critical point of a lattice model
• Many-body spin Berry phases emerging from the $\pi$-flux state: antiferromagnetic/valence-bond-solid competition
• Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
• Theory of the nodal nematic quantum phase transition in superconductors
• Dirac Fermions with Competing Orders: Non-Landau Transition with Emergent Symmetry
• Four loop renormalization of the Gross-Neveu model
• Critical behavior of the QED${}_3$-Gross-Neveu model: Duality and deconfined criticality
• Four loop MSbar mass anomalous dimension in the Gross-Neveu model