Hybrid Monte Carlo Simulations of Graphene
Summary
We give a discussion on the Hybrid Monte Carlo simulations of the tight binding model with Coulomb
interactions, for the electronic properties of Graphene. The aim of our simulations is to determine
the phase transition in which Graphene goes from a semimetal to an insulator through spontaneous
breaking of sublattice symmetry. This is done non-perturbatively using lattice field theory techniques,
working in the path-integral formalism with discrete euclidean time. We explain the method by
[Brower, Rebbi and Schaich, arXiv:1101.5131v1, 26 Jan 2011] through which the theory of Graphene
can be written in a form independent of a sign problem. An implementation of this method has been
made in Julia, and can be found in [https://github.com/Rik-Breebaart/GrapheneHMC.git]. Our
measurements show no clear phase-transition in the order parameters for this sublattice symmetry
breaking. However, the system sizes on which the simulation have been performed where to small to
make conclusive prediction on the presence and critical value of the phase-transition.