We use exact quantum Monte Carlo simulations to demonstrate that the N\'eel ground state of an antiferromagnetic SU(2) spin-21 Heisenberg model on the honeycomb lattice can be destroyed by a coupling to quantum phonons. We find a clear first-order transition to a valence-bond-solid state with Kekul\'e order instead of a deconfined quantum critical point. However, quantum lattice fluctuations can drive the transition towards weakly first-order, revealing a tunability of the transition by the retardation of the interaction. In contrast to the one-dimensional case, our phase diagram in the adiabatic regime is qualitatively different from the frustrated J1-J2 model. Our results suggest that a coupling to bond phonons can induce Kekul\'e order in Dirac systems.
@article{arxiv.2009.12393,
title = {Valence-Bond Order in a Honeycomb Antiferromagnet Coupled to Quantum Phonons},
author = {Manuel Weber},
journal= {arXiv preprint arXiv:2009.12393},
year = {2021}
}