We study the instabilities to the conformal critical point of an exactly solvable family of Gross-Neveu models. Using conformal field theory techniques, we construct the zero-temperature phase diagram and identify the superconducting and charge neutral ordered phases that destabilize the critical point. Both instabilities appear only when the fermions are strongly renormalized, above a critical anomalous dimension. A higher fermion anomalous dimension also raises the critical degree of time-reversal-symmetry breaking required to suppress superconductivity, indicating that pairing becomes more robust with stronger renormalization.
We study the instabilities to the conformal critical point of an exactly solvable family of Gross-Neveu models. Using conformal field theory techniques, we construct the zero-temperature phase diagram and identify the superconducting and charge neutral ordered phases that destabilize the critical point. Both instabilities appear only when the fermions are strongly renormalized, above a critical anomalous dimension. A higher fermion anomalous dimension also raises the critical degree of time-reversal-symmetry breaking required to suppress superconductivity, indicating that pairing becomes more robust with stronger renormalization.
We study two-dimensional massless Dirac fermions at neutrality, coupled to bosonic modes through a Yukawa interaction. We then examine the intriguing possibility that such a system, devoid of carriers at zero temperature, might nevertheless exhibit superconductivity. Remarkably, we find that superconductivity emerges in the vicinity of Gross-Neveu quantum criticality, provided the fermions cease to behave as well-defined quasiparticles, that is, once their anomalous dimension in the normal state becomes sufficiently large. In other words, well-defined fermions do not superconduct, whereas ill-defined ones do. We analyze four symmetry-distinct bosonic modes, each capable of driving normal-state criticality and, in three of the four cases, giving rise to a distinct superconducting phase. While phase fluctuations are strong in this regime, we argue that they do not destroy the superconducting state. We further characterize the resulting pairing states for a concrete Dirac model of spin-orbit coupled systems with orbitals of different parity. Our results are obtained using the Sachdev-Ye-Kitaev (SYK)-inspired framework for Dirac systems introduced by Kim [Dirac fast scramblers, ], which provides a controlled approach to the strongly coupled regime of Dirac fluids near Gross-Neveu criticality.
A second-order phase transition for the three-dimensional Gross-Neveu model is established for one fermion species, N=1. This transition breaks a paritylike discrete symmetry. It constitutes its peculiar universality class with critical exponent $\ensuremath{\nu}=0.63$ and scalar and fermionic anomalous dimensions ${\ensuremath{\eta}}_{\ensuremath{\sigma}}=0.31$ and ${\ensuremath{\eta}}_{\ensuremath{\psi}}=0.11,$ respectively. We also compute critical exponents for other N. Our results are based on exact renormalization-group equations.
We grow the web of dualities for conformal field theories (CFTs) in 2+1 spacetime dimensions to include quantum critical transitions of Dirac fermions. Our construction uses the seed duality, equating a free Dirac fermion with a complex boson coupled to a Chern-Simons gauge field, to express various Gross-Neveu-Yukawa (GNY) critical points of N fermions in terms of the same number of complex bosons and partner gauge fields. In some instances, monopole operators appear explicitly in the dual action, such as for the superconducting transition of a single Dirac fermion, which is a CFT with emergent supersymmetry. We match phase diagrams, symmetries and their anomalies. By further gauging certain symmetries, we derive offspring dualities. For example, starting with the duality for the regular GNY transition of 2 Dirac fermions, we arrive at the duality between a Neel-to-VBS deconfined quantum critical point and a gauged-Gross-Neveu transition. Finally, we use a large-N expansion for monopole operators, and compare with known scaling dimensions in the simplest single-flavour GNY transition.
The fluctuations-driven continuous quantum criticality has sparked tremendous interest in condensed matter physics. It has been verified that the gapless fermions fluctuations can change the nature of phase transition at criticality. In this paper, we study the fermionic quantum criticality with enlarged Ising×Ising fluctuations in honeycomb lattice materials. The Gross-Neveu-Yukawa theory for the multicriticality between the semimetallic phase and two ordered phases that break Ising symmetry is investigated by employing perturbative renormalization group approach. We first determine the critical range in which the quantum fluctuations may render the phase transition continuous. We find that the Ising criticality is continuous only when the flavor numbers of four-component Dirac fermions Nf≥1/4. Using the ε expansion in four space-time dimensions, we then study the Ising×Ising multicriticality stemming from the symmetry-breaking electronic instabilities. We analyze the underlying fixed-point structure and compute the critical exponents for the Ising×Ising Gross-Neveu-Yukawa universality class. Further, the correlation scaling behavior for the fermion bilinear on the honeycomb lattice at the multicritical point are also briefly discussed.
We investigate the relativistic SO(2)- and SO(3)-invariant Gross-Neveu-Yukawa field theories for real, rank-two, symmetric, traceless tensor order parameters coupled to Nf flavors of two-component Dirac fermions. These field theories arise as an effective description of fractionalized spin-orbital liquids. The two theories are the simplest and special cases of the more general class of field theories with SO(N) symmetric tensor order parameter coupled to Dirac fermions, in which the symmetry is low enough to allow only one and not the usual two quartic self-interaction terms. Using a two-loop renormalization group near the upper critical dimension, we demonstrate that the theory exhibits an exotic critical fixed point for N=3 and the concomitant continuous phase transition for any value of Nf. For N=2 the theory is equivalent to the chiral XY model. We discuss the crucial role of the symmetry-allowed sextic self-interactions in the selection of the ground state configuration in the case of SO(3). The universal quantities such as the anomalous dimensions of order parameters and fermions, the correlation length exponent, and the mass gap ratio between order parameter and fermion masses are computed up to ${\ensuremath{\epsilon}}^{2}$ order.
We study the critical properties of the QED3-Gross-Neveu model with 2N flavors of two-component Dirac fermions coupled to a massless scalar field and a U(1) gauge field. For N=1, this theory has recently been suggested to be dual to the SU(2) noncompact CP1 model that describes the deconfined phase transition between the N\'eel antiferromagnet and the valence bond solid on the square lattice. For N=2, the theory has been proposed as an effective description of a deconfined critical point between chiral and Dirac spin liquid phases, and may potentially be realizable in spin-1/2 systems on the kagome lattice. We demonstrate the existence of a stable quantum critical point in the QED3-Gross-Neveu model for all values of N. This quantum critical point is shown to escape the notorious fixed-point annihilation mechanism that renders plain QED3 (without scalar-field coupling) unstable at low values of N. The theory exhibits an upper critical space-time dimension of four, enabling us to access the critical behavior in a controlled expansion in the small parameter $\ensuremath{\epsilon}=4\ensuremath{-}D$. We compute the scalar-field anomalous dimension ${\ensuremath{\eta}}_{\ensuremath{\phi}}$, the correlation-length exponent $\ensuremath{\nu}$, as well as the scaling dimension of the flavor-symmetry-breaking bilinear $\overline{\ensuremath{\psi}}{\ensuremath{\sigma}}^{z}\ensuremath{\psi}$ at the critical point, and compare our leading-order estimates with predictions of the conjectured duality.