Lattice field theory simulations of graphene

Details Lattice field theory simulations of graphene Lattice field theory simulations of graphene

2009-01-06

arxiv.org/abs/0901.0584v2

Phys. Rev. B 79, 165425 (2009)

Physics

Condensed Matter

Strongly Correlated Electrons

14 pages, 7 figures. Published version freely available if accessed via http://physics.aps.org/articles/v2/30

Scientific paper

10.1103/PhysRevB.79.165425

We discuss the Monte Carlo method of simulating lattice field theories as a means of studying the low-energy effective theory of graphene. We also report on simulational results obtained using the Metropolis and Hybrid Monte Carlo methods for the chiral condensate, which is the order parameter for the semimetal-insulator transition in graphene, induced by the Coulomb interaction between the massless electronic quasiparticles. The critical coupling and the associated exponents of this transition are determined by means of the logarithmic derivative of the chiral condensate and an equation-of-state analysis. A thorough discussion of finite-size effects is given, along with several tests of our calculational framework. These results strengthen the case for an insulating phase in suspended graphene, and indicate that the semimetal-insulator transition is likely to be of second order, though exhibiting neither classical critical exponents, nor the predicted phenomenon of Miransky scaling.

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