Valence bond order in a honeycomb antiferromagnet coupled to quantum phonons
We use exact quantum Monte Carlo simulations to demonstrate that the Néel ground state of an antiferromagnetic SU(2) spin-1/2 Heisenberg model on the honeycomb lattice can be destroyed by a coupling to quantum phonons. Here, 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 –J 2 model. Our results suggest that a coupling to bond phonons can induce Kekulé order in Dirac systems.