Long before the discovery of its extraordinary properties, graphene - i.e., single sheet graphite - had long been the textbook exercise of a symmetry-induced semimetallic state of noninteracting electrons with nearest neighbor hopping *t* in the honeycomb lattice[1]. Nowadays the accepted picture of correlated electrons in graphene comes from quantum Monte Carlo simulation of an idealized and simplified model on a lattice. In this model, by stretching graphene, namely by decreasing the hopping *t* between nearest neighbor carbons, the electronic system becomes an antiferromagnetic Mott insulator at a critical value of the ratio *U/t* = 3.84(1)[2, 3], where *U* is the Coulomb repulsion. It is therefore timely to investigate theoretically this interesting system by a more realistic simulation, also because, recently, it appears experimentally feasible to isotropically stretch graphene, overcoming its extremely large two-dimensional bulk modulus, originated in its harder-than-diamond sigma bonds.

In this paper, we study for the first time electronic and lattice structures of a single-layer graphene under isotropic stretching, by means of first-principles quantum Monte Carlo simulation. The competition between the totally symmetric state, the antiferromagnetic state, and a Peierls state with lattice distortion is explored by calculating the enthalpy as a function of tensile force at zero temperature. Preliminary results indicate that the antiferromagnetic state is less stable than the other states, while a transition between the totally symmetric state and the Peierls state is found at a certain strength of the tensile force.

[1] F. Bassani and G. Pastori Paravicini, Electronic States and Optical Transitions in Solids (Pergamon Press, 1975).

[2] S. Sorella, Y. Otsuka, and S. Yunoki, Absence of a spin liquid phase in the Hubbard model on the honeycomb lattice, Sci. Rep. 2, 992 (2012).

[3] Y. Otsuka, S. Yunoki, and S. Sorella, Universal Quantum Criticality in the Metal-Insulator Transition of Two-Dimensional Interacting Dirac Electrons, Phys. Rev. X 6, 011029 (2016).