Gauge-field-assisted Kekul\'e quantum criticality

TL;DR

This paper investigates the nature of the quantum phase transition in a honeycomb lattice system with Dirac fermions coupled to Kekule9 order, revealing conditions under which the transition can be continuous or first-order, especially considering gauge field effects.

Contribution

It provides a detailed renormalization group analysis of the Kekule9 quantum criticality, highlighting the role of gauge fields and fermion number in determining the transition's nature.

Findings

Quantum fluctuations can make the transition continuous far from 3+1 dimensions.

Presence of gauge fields induces quantum critical behavior near 3+1 dimensions.

Higher-loop RG analysis of the cubic coupling for large fermion numbers.

Abstract

We study the quantum phase transition of $U(1)$ - charged Dirac fermions Yukawa-coupled to the Kekul\'e 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 Kekul\'e 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.