Fermionic multicriticality near Kekulé valence-bond ordering in honeycomb lattice

Abstract

We analyze the possibility of emergent quantum multicritical points (MCPs) with enlarged chiral symmetry, when strongly interacting gapless Dirac fermions acquire comparable propensity toward the nucleation of Kekulé valence-bond solid (KVBS) and charge-density-wave ($N_b=1$) or $s$-wave pairing ($N_b=2$) or anti-ferromagnet ($N_b=3$) in honeycomb lattice, where $N_b$ counts the number of bosonic order parameter components. Besides the cubic terms present in the order parameter description of KVBS due to the breaking of a discrete $Z_3$ symmetry, quantum fluctuations generate new cubic vertices near the high symmetry MCPs. All cubic terms are strongly relevant at the bare level near three spatial dimensions, about which we perform a leading order renormalization group analysis of coupled Gross-Neveu-Yukawa field theory. We show that due to non-trivial Yukawa interactions among gapless bosonic and fermionic degrees of freedom, all cubic terms ultimately become irrelevant at an $O(2+N_b)$ symmetric MCP, near two spatial dimensions, where $N_b=1,2,3$. Therefore, MCPs with an enlarged $O(2+N_b)$ symmetry near KVBS ordering are stable.

6 Pages, 2 Figures: Published version in Phys. Rev. B (Supplementary: As ancillary file)

References in corpus (16)

• The electronic properties of graphene
• Topological Mott Insulators
• Interactions and phase transitions on graphene's honeycomb lattice
• Electron fractionalization in two-dimensional graphenelike structures
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• Theory of interacting electrons on the honeycomb lattice
• Density waves and Cooper pairing on the honeycomb lattice
• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• Emergent space-time supersymmetry in 3D Weyl and 2D Dirac semimetals
• Unconventional superconductivity on honeycomb lattice: the theory of Kekule order parameter
• Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
• Quantum superconducting criticality in graphene and topological insulators
• Dirac Fermions with Competing Orders: Non-Landau Transition with Emergent Symmetry
• Ising and Gross-Neveu model in next-to-leading order
• The emergence of a universal limiting speed
• Note on "Quantum superconducting criticality in graphene and topological insulators"

Cited by in corpus (1)

• Fermionic criticality with enlarged fluctuations in Dirac semimetals