We use exact quantum Monte Carlo simulations to demonstrate that the Néel ground state of an antiferromagnetic SU(2) spin-$\frac{1}{2}$ 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 Kekulé 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 $J_1\text{−}{J}_2$ model. Our results suggest that a coupling to bond phonons can induce Kekulé order in Dirac systems.

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• Frustrated magnetism
• Magnetic phase transitions
• Peierls transition
• Phase diagrams
• Phonons
• Quantum phase transitions
• Antiferromagnets
• Honeycomb lattice
• Strongly correlated systems
• Quantum Monte Carlo
• Spin lattice models