Fermionic criticality with enlarged fluctuations in Dirac semimetals

Abstract

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$\times$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 $N_f\ge 1/4$. Using the $\epsilon$ expansion in four space-time dimensions, we then study the Ising$\times$Ising multicriticality stemming from the symmetry-breaking electronic instabilities. We analyze the underlying fixed-point structure and compute the critical exponents for the Ising$\times$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.

10 pages, 2 figures

References in corpus (20)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Topological Mott Insulators
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Electron fractionalization in two-dimensional graphenelike structures
• Theory of interacting electrons on the honeycomb lattice
• Density waves and Cooper pairing on the honeycomb lattice
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Emergent space-time supersymmetry in 3D Weyl and 2D Dirac semimetals
• Quantum Critical Behaviour in a Graphene-like Model
• Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
• Dirac Fermions with Competing Orders: Non-Landau Transition with Emergent Symmetry
• Four loop renormalization of the Gross-Neveu model
• Gauge-field-assisted Kekulé quantum criticality
• The Renormalization Group Studies on Four Fermion Interaction Instabilities on Algebraic Spin Liquids
• Designer Monte Carlo Simulation for Gross-Neveu Transition
• Fermionic multicriticality near Kekulé valence-bond ordering in honeycomb lattice
• Fermion-induced quantum critical point in Dirac semimetals: a sign-problem-free quantum Monte Carlo study
• Emergent Symmetry and Tricritical Points near the deconfined Quantum Critical Point