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.

arXiv comment6 Pages, 2 Figures: Published version in Phys. Rev. B (Supplementary: As ancillary file)

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• Finite-system Multicriticality at the Superradiant Quantum Phase Transition
• Quantum phase transitions in Dirac fermion systems
• Gross-Neveu Heisenberg criticality: dynamical generation of quantum spin Hall masses
• Valence-Bond Order in a Honeycomb Antiferromagnet Coupled to Quantum Phonons
• Emergent symmetries and coexisting orders in Dirac fermion systems
• Novel criticality of Dirac fermions from lattice symmetry breaking
• Fermion-induced Dynamical Critical Point
• Novel criticality of Dirac fermions in the presence of emergent gauge fields
• Fermion-induced quantum critical point in the Landau-Devonshire model
• Charge order and Mott insulating ground states in small-angle twisted bilayer graphene
• Kekulé valence bond order in the Hubbard model on the honeycomb lattice with possible lattice distortions for graphene
• Critical structure and emergent symmetry of Dirac fermion systems
• Fermionic criticality with enlarged fluctuations in Dirac semimetals