Quantum and Classical Ripples in Graphene*

Flexural fluctuations and thermal ripples of suspended graphene are known to be gigantic at room temperature, but their quantum counterpart at ultralow temperatures, addressed so far mostly by asymptotic RG techniques, are still in need of a realistic and quantitative description and comparison on the same grounds. Here we present fully atomistic
quantum Path Integral Monte Carlo simulations of freestanding graphene, which demonstrate upon cooling the progressive quantum evolution of heigth and angular rippling fluctuations, compared with a reference classical Monte Carlo. Even though the classical-quantum crossover takes place at ever-decreasing temperatures for ever-increasing wavelengths so that a completely quantum regime is never attained, the dramatic replacement of classical by quantum fluctuations and the resulting modification of the low temperature landscape, accessible in principle to scattering techniques, are quantitatively predicted.