# Fermionic multicriticality near Kekul\'{e} valence-bond ordering in honeycomb lattice

## TL;DR

This paper investigates the stability of emergent quantum multicritical points with enlarged symmetry in honeycomb lattice systems, showing that certain cubic terms become irrelevant near two dimensions, leading to stable MCPs with enhanced symmetry.

## Contribution

It demonstrates that quantum fluctuations render cubic terms irrelevant at MCPs with $O(2+N_b)$ symmetry, establishing their stability in honeycomb lattice models.

## Key findings

- Cubic terms are relevant near three dimensions but become irrelevant near two dimensions.
- Enlarged $O(2+N_b)$ symmetric MCPs are stable due to Yukawa interactions.
- Quantum fluctuations suppress discrete symmetry breaking at MCPs.

## 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 Kekul\'{e} 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.