We present evidence, from Lattice Monte Carlo simulations of the phase diagram of graphene as a function of the Coulomb coupling between quasiparticles, that graphene in vacuum is likely to be an insulator. We find a semimetal-insulator transition at α crit g = 1.11 ± 0.06, where α g ≃ 2.16 in vacuum, and α g ≃ 0.79 on a SiO 2 substrate. Our analysis uses the logarithmic derivative of the order parameter, supplemented by an equation of state. The insulating phase disappears above a critical number of four-component fermion flavors 4 < N crit f < 6. Our data are consistent with a second-order transition. Graphene, a carbon allotrope with a two-dimensional honeycomb structure, has become an important player at the forefront of condensed matter physics, drawing the attention of theorists and experimentalists alike due to its challenging nature as a many-body problem, its unusual electronic properties and possible technological applications (see Refs. [1, 2] and references therein). Graphene also belongs to a large class of planar condensed-matter systems, which includes other graphite-related materials as well as high-T c superconductors.A distinctive feature of graphene is that its band structure contains two degenerate 'Dirac points', in the vicinity of which the dispersion is linear, as in relativistic theories [3]. The low-energy excitations in graphene are thus Dirac quasiparticles of Fermi velocity v ≃ c/300, where c is the speed of light in vacuum. These are described by the Euclidean actionwhere g 2 = e 2 /ǫ 0 for graphene in vacuum, ψ a is a four-component Dirac field in 2+1 dimensions, A 0 is a Coulomb field in 3+1 dimensions, N f = 2 for real graphene, andwhere the Dirac matrices γ µ satisfy the Euclidean Clifford algebra {γ µ , γ ν } = 2δ µν . The strength of the Coulomb interaction is controlled (as can be shown by rescaling t and A 0 ) by α g = e 2 /(4πvǫ 0 ), which is the graphene analogue of the fine-structure constant α ≃

The excited state of the 12 C nucleus known as the "Hoyle state" constitutes one of the most interesting, difficult and timely challenges in nuclear physics, as it plays a key role in the production of carbon via fusion of three alpha particles in red giant stars. In this letter, we present ab initio lattice calculations which unravel the structure of the Hoyle state, along with evidence for a lowlying spin-2 rotational excitation. For the 12 C ground state and the first excited spin-2 state, we find a compact triangular configuration of alpha clusters. For the Hoyle state and the second excited spin-2 state, we find a "bent-arm" or obtuse triangular configuration of alpha clusters. We also calculate the electromagnetic transition rates between the low-lying states of 12 C.PACS numbers: 21.10. Dr, 21.60.De, 26.20.Fj The carbon nucleus 12 C is produced by fusion of three alpha particles in red giant stars. However, without resonant enhancement the triple alpha reaction is too slow to account for the observed abundance of carbon in the Universe. In the early 1950's,Öpik and Salpeter noted independently that the first step of merging two alpha particles is enhanced by the formation of [6], which would imply low-lying rotational excitations of even parity. Other ideas also exist for the structure of the Hoyle state, such as a diffuse trimer of alpha particles [7]. Recently, the spin-2 excitation of the Hoyle state has attracted considerable interest from several experimental groups [8][9][10][11][12].We have recently presented an ab initio lattice calculation of the Hoyle state [13] where the low-lying spectrum of 12 C was explored using the framework of chiral effective field theory and Monte Carlo lattice calculations. However the central question regarding the alpha cluster structure of the Hoyle state remained unsolved, perhaps the greatest remaining challenge in ab initio nuclear theory. In this letter, we announce a major innovation of the lattice method that constructs and tests a wide class of nuclear wave functions explicitly. We present ab initio lattice results that resolve questions about the structure of the Hoyle state and the existence of rotational excitations. We also find evidence for a low-lying spin-2 rotational excitation of the Hoyle state. For the Hoyle state and its spin-2 excitation, we find strong overlap with a "bent-arm" or obtuse triangular configuration of alpha clusters. This is in contrast with the 12 C ground state and the first spin-2 state, where we note strong overlap with a compact triangular configuration of alpha clusters. We also calculate the electromagnetic transition rates among the low-lying even-parity states of 12 C. Our lattice results can be compared with other recent theoretical calculations for the low-lying spectrum of 12 C using the no-core shell model [14,15] and variational calculations using Fermionic Molecular Dynamics [16,17].Chiral effective field theory treats the interactions of protons and neutrons as a systematic expansion in powers of nucleon momenta...

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.

We extend Nuclear Lattice Effective Field Theory (NLEFT) to medium-mass nuclei, and present results for the ground states of alpha nuclei from 4 He to 28 Si, calculated up to next-to-next-to-leading order (NNLO) in the EFT expansion. This computational advance is made possible by extrapolations of lattice data using multiple initial and final states. For our soft two-nucleon interaction, we find that the overall contribution from multi-nucleon forces must change sign from attractive to repulsive with increasing nucleon number. This effect is not produced by three-nucleon forces at NNLO, but it can be approximated by an effective four-nucleon interaction. We discuss the convergence of the EFT expansion and the broad significance of our findings for future ab initio calculations.

We present ab initio lattice calculations of the low-energy even-parity states of 16O using chiral nuclear effective field theory. We find good agreement with the empirical energy spectrum, and with the electromagnetic properties and transition rates. For the ground state, we find that the nucleons are arranged in a tetrahedral configuration of alpha clusters. For the first excited spin-0 state, we find that the predominant structure is a square configuration of alpha clusters, with rotational excitations that include the first spin-2 state.