Chiral symmetry breaking in monolayer graphene by strong coupling expansion of compact and non-compact U(1) lattice gauge theories

Araki, Yasufumi

doi:10.1016/j.aop.2011.01.002

Cited by 25 publications

(38 citation statements)

References 47 publications

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“…[46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62] Typically, three different approaches are used: (i) direct numerical work using lattice QCD type calculations; [51][52][53][54][55][56] (ii) using some sort of Schwinger-Dyson theory, 57,58,[63][64][65][66] which involves solving an integral equation built from some infinite subset of (usually ladder-type) diagrams; and (iii) mapping the strong-coupling problem onto some known strongcoupling field theoretic model (e.g. the Gross-Neveu model 67 ) through some ad-hoc approximations.…”

Section: 18mentioning

confidence: 99%

Effective field theory, three-loop perturbative expansion, and their experimental implications in graphene many-body effects

et al. 2014

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Many-body electron-electron interaction effects are theoretically considered in monolayer graphene from a continuum effective field-theoretic perspective by going beyond the standard leading-order single-loop perturbative renormalization group (RG) analysis. Given that the effective (bare) coupling constant (i.e. the fine structure constant) in graphene is of order unity, which is neither small to justify a perturbative expansion nor large enough for strong-coupling theories to be applicable, the problem is a difficult one, with some similarity to 2+1-dimensional strong-coupling quantum electrodynamics (QED). In this work, we take a systematic and comprehensive analytical approach in theoretically studying graphene many-body effects, primarily at the Dirac point (i.e., in undoped, intrinsic graphene), by going up to three loops in the diagrammatic expansion to both ascertain the validity of a perturbative expansion in the coupling constant and to develop an RG theory that can be used to estimate the actual quantitative renormalization effect to higher-order accuracy. Electronelectron interactions are expected to play an important role in intrinsic graphene due to the absence of screening at the Dirac (charge neutrality) point, potentially leading to strong deviations from the Fermi liquid description around the charge neutrality point where the graphene Fermi velocity should manifest an ultraviolet logarithmic divergence because of the linear band dispersion. While no direct signatures for non-Fermi liquid behavior at the Dirac point have yet been observed experimentally, there is ample evidence for the interaction-induced renormalization of the graphene velocity as the Dirac point is approached by lowering the carrier density. We provide a critical comparison between theory and experiment, using both higher-order diagrammatic and RPA (i.e., infinite-order bubble diagrams) calculations, emphasizing future directions for a deeper understanding of the graphene effective field theory. We find that while the one-loop RG analysis gives reasonable quantitative agreement with the experimental data, both for graphene in vacuum and graphene on substrates, particularly when dynamical screening effects and finite carrier density effects are incorporated in the theory through the random phase approximation, the two-loop analysis reveals an interacting strong-coupling critical point in graphene suspended in vacuum signifying either a quantum phase transition or a breakdown of the weak-coupling renormalization group approach. By adapting a version of Dyson's argument for the breakdown of the QED perturbative expansion to the case of graphene, we show that in contrast to QED where the asymptotic perturbative series in the coupling constant converges to at least 137 orders (and possibly to much higher order) before diverging in higher orders, the graphene perturbative series in the coupling constant may manifest asymptotic divergence already in the first or second order in the coupling constant, favoring the conclusion that per...

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Section: 18mentioning

confidence: 99%

Effective field theory, three-loop perturbative expansion, and their experimental implications in graphene many-body effects

et al. 2014

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“…Experiments have provided evidence that graphene in vacuum is in fact a conductor [28,29], while analytical calculations [30][31][32][33][34] and simulations [13-15, 18, 19, 25], which assumed that the electromagnetic interactions of π-band electrons (the relevant degrees of freedom for the electronic properties) are essentially unmodified Coulomb interactions, supported the scenario of a gapped phase for α eff > α c ≈ 1, well within the accessible region. The origin of this disparity must thus be investigated.…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo simulation of the tight-binding model of graphene with partially screened Coulomb interactions

Smith

Smekal

2014

Phys. Rev. B

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We report on Hybrid-Monte-Carlo simulations of the tight-binding model with long-range Coulomb interactions for the electronic properties of graphene. We investigate the spontaneous breaking of sublattice symmetry corresponding to a transition from the semimetal to an antiferromagnetic insulating phase. Our short-range interactions thereby include the partial screening due to electrons in higher energy states from ab initio calculations based on the constrained random phase approximation [T. O. Wehling et al., Phys. Rev. Lett. 106, 236805 (2011)]. In contrast to a similar previous Monte-Carlo study [M. V. Ulybyshev et al., Phys. Rev. Lett. 111, 056801 (2013)] we also include a phenomenological model which describes the transition to the unscreened bare Coulomb interactions of graphene at half filling in the long-wavelength limit. Our results show, however, that the critical coupling for the antiferromagnetic Mott transition is largely insensitive to the strength of these longrange Coulomb tails. They hence confirm the prediction that suspended graphene remains in the semimetal phase when a realistic static screening of the Coulomb interactions is included.

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“…This contrasts with the result of the strong coupling expansion in graphene. 35,36 In graphene, the rate of decrease of σ from β = 0 to β = 0.5 is about 60%, 36 whereas that of our model is about 3% at r = 0.2. In other words, in our model, the topological insulator phase survives in the strong coupling limit, although graphene undergoes the semimetal-insulator transition in the strong coupling region.…”

Section: Numerical Resultsmentioning

confidence: 88%

“…In such a case, the strong coupling lattice gauge theory is applied. [30][31][32][33][34][35][36][37][38] The chiral condensate is the order parameter for the insulator-semimetal transition in the lattice gauge theory. It is noteworthy that lattice Monte Carlo studies show a quantitatively correct critical value of the coupling strength below which the system becomes gapless 31,32,38 (graphene on a SiO 2 substrate is conducting).…”

Section: Introductionmentioning

confidence: 99%

Strong coupling expansion in a correlated three-dimensional topological insulator

et al. 2013

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Motivated by recent studies which show that topological phases may emerge in strongly correlated electron systems, we theoretically study the strong electron correlation effect in a three-dimensional topological insulator, where the effective Hamiltonian can be described by the Wilson fermions. We adopt a 1/r long-range Coulomb interaction as the interaction between the bulk electrons. Based on the U(1) lattice gauge theory, the strong coupling expansion is applied by assuming that the effective interaction is strong. It is shown that the effect of the Coulomb interaction is equivalent to the renormalization of the bare mass of the Wilson fermions and, as a result, the topological insulator phase survives in the strong coupling limit.

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Chiral symmetry breaking in monolayer graphene by strong coupling expansion of compact and non-compact U(1) lattice gauge theories

Cited by 25 publications

References 47 publications

Effective field theory, three-loop perturbative expansion, and their experimental implications in graphene many-body effects

Effective field theory, three-loop perturbative expansion, and their experimental implications in graphene many-body effects

Monte Carlo simulation of the tight-binding model of graphene with partially screened Coulomb interactions

Strong coupling expansion in a correlated three-dimensional topological insulator

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