Kekule valence bond order in strained graphene

We report the results of a Quantum Monte Carlo (QMC) study of the Hubbard model on a honeycomb lattice with lattice deformation. The most stable pattern of lattice deformation was obtained by considering all the patterns of lattice distortion allowed by the reflection symmetry. The resulting phase diagram reveals a region in which the Kekulé-type valence bond solid (VBS) phase is stabilized as the electron-electron interaction increases. This finding suggests that in real graphene, a transition from a semimetallic phase to a VBS-type insulator may occur when negative pressure is applied.