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Quantum Critical Behaviour in a Graphene-like Model

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arxiv 0806.4877 v1 pith:DTCP7EX2 submitted 2008-06-30 cond-mat.str-el cond-mat.mes-hallhep-lat

Simon Hands , Costas Strouthos This is my paper · ORCID
classification cond-mat.str-elcond-mat.mes-hallhep-lat
keywords criticalbehaviourgraphenemodelquantumstrongtransitionapproximately
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We present the first results of numerical simulations of a 2+1 dimensional fermion field theory based on a recent proposal for a model of graphene, consisting of N_f four-component Dirac fermions moving in the plane and interacting via an instantaneous Coulomb interaction. In the strong-coupling limit we identify a critical number of flavors N_fc=4.8(2) separating an insulating from a conducting phase. This transition corresponds to the location of a quantum critical point, and we use a fit to the equation of state for the chiral order parameter to estimate the critical exponents. Next we simulate N_f=2 corresponding to real graphene, and approximately locate a transition from strong to weak coupling behaviour. Strong correlations are evident in the weak-coupling regime.

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  1. Fermions and the Renormalisation Group at Large N

    hep-th 2025-02 conditional novelty 7.0 of 10

    At large N, fermionic quantum field theories have exact effective actions depending only on flavour-singlet fermion bilinears, making the local potential approximation exact and yielding new conformal fixed points.

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