Gauge-field-assisted Kekulé quantum criticality

Abstract

We study the quantum phase transition of $U(1)$ - charged Dirac fermions Yukawa-coupled to the Kekulé valence bond solid order parameter with $Z_3$ symmetry of the honeycomb lattice. The symmetry allows for the presence of the term in the action which is cubic in the Kekulé order parameter, and which is expected to prevent the quantum phase transition in question from being continuous. The Gross-Neveu-Yukawa theory for the transition is investigated using a perturbative renormalization group and within the $\epsilon$ expansion close to four space-time dimensions. For a vanishing $U(1)$ charge we show that quantum fluctuations may render the phase transition continuous only sufficiently far away from 3+1 dimensions, where the validity of the conclusions based on the leading order $\epsilon$ expansion appear questionable. In the presence of a fluctuating gauge field, on the other hand, we find quantum critical behavior even at weak coupling to appear close to 3+1 dimensions, that is, within the domain of validity of the perturbation theory. We also determine the renormalization group scaling of the cubic coupling at higher-loop orders and for a large number of Dirac fermions for vanishing charge.

8 pages, 4 figures

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Cited by in corpus (7)

• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Momentum dependence of quantum critical Dirac systems
• Finite-temperature valence-bond-solid transitions and thermodynamic properties of interacting SU($2N$) Dirac fermions
• Fermion-induced quantum critical point in Dirac semimetals: a sign-problem-free quantum Monte Carlo study
• Functional RG approach to the Potts model
• Fermion enhanced first-order phase transition and chiral Gross-Neveu tricritical point
• Fermionic criticality with enlarged fluctuations in Dirac semimetals