Numerical evidence of conformal phase transition in graphene with long-range interactions
Abstract
Using state of the art Hybrid-Monte-Carlo (HMC) simulations we carry out an unbiased study of the competition between spin-density wave (SDW) and charge-density wave (CDW) order in suspended graphene. We determine that the realistic inter-electron potential of graphene must be scaled up by a factor of roughly 1.6 to induce a semimetal-SDW phase transition and find no evidence for CDW order. A study of critical properties suggests that the universality class of the three-dimensional chiral Heisenberg Gross-Neveu model with two fermion flavors, predicted by renormalization group studies and strong-coupling expansion, is unlikely to apply to this transition. We propose that our results instead favor an interpretation in terms of a conformal phase transition. In addition, we describe a variant of the HMC algorithm which uses exact fermionic forces during molecular dynamics trajectories and avoids the use of pseudofermions. Compared to standard HMC this allows for a substantial increase of the integrator stepsize while achieving comparable Metropolis acceptance rates and leads to a sizable performance improvement.
Keywords
Cite
@article{arxiv.1812.06435,
title = {Numerical evidence of conformal phase transition in graphene with long-range interactions},
author = {Pavel Buividovich and Dominik Smith and Maksim Ulybyshev and Lorenz von Smekal},
journal= {arXiv preprint arXiv:1812.06435},
year = {2019}
}
Comments
revised version, accepted for publication in Phys. Rev. B