We report on the results of the first-principles numerical study of spontaneous breaking of chiral (sublattice) symmetry in suspended monolayer graphene due to electrostatic interaction, which takes into account the screening of Coulomb potential by electrons on σ orbitals. In contrast to the results of previous numerical simulations with unscreened potential, we find that suspended graphene is in the conducting phase with unbroken chiral symmetry. This finding is in agreement with recent experimental results by the Manchester group [D. C. Elias et al., Nat. Phys. 7, 701 (2011); A. S. Mayorov et al., Nano Lett. 12, 4629 (2012)]. Further, by artificially increasing the interaction strength, we demonstrate that suspended graphene is quite close to the phase transition associated with spontaneous chiral symmetry breaking, which suggests that fluctuations of chirality and nonperturbative effects might still be quite important.

We report on the direct numerical measurements of the conductivity of graphene monolayer. Our numerical simulations are performed in the effective lattice field theory with noncompact 3 + 1dimensional Abelian lattice gauge fields and 2 + 1-dimensional staggered lattice fermions. The conductivity is obtained from the Green-Kubo relations using the Maximum Entropy Method. We find that in a phase with spontaneously broken sublattice symmetry the conductivity rapidly decreases. For the largest value of the coupling constant used in our simulations g = 4.5, the DC conductivity is less than the DC conductivity in the weak-coupling phase (at g < 3.5) by at least three orders of magnitude.

The axial magnetic field, which couples to left-and right-handed fermions with opposite signs, may generate an equilibrium dissipationless energy flow of fermions in the direction of the field even in the presence of interactions. We report on numerical observation of this Axial Magnetic Effect in quenched SU (2) lattice gauge theory. We find that in the deconfinement (plasma) phase the energy flow grows linearly with the increase of the strength of the axial magnetic field. In the confinement (hadron) phase the Axial Magnetic Effect is absent. Our study indirectly confirms the existence of the Chiral Vortical Effect since both these effects have the same physical origin related to the presence of the gravitational anomaly.PACS numbers: 12.38.Mh, 47.75.+f, 11.15.Ha Anomalies belong to the most characteristic and fundamental properties of relativistic quantum field theories. They signal an incompatibility between quantization and the symmetries present at the classical level. While the effects of anomalies in vacuum are well understood it has only recently been fully appreciated that anomalies play also an extraordinary important role at finite temperature and density. In particular they give rise to new non-dissipative transport phenomena. The most well-known of these is the so-called Chiral Magnetic Effect (CME) [1], describing the generation of an electric current parallel to a magnetic field in the presence of an imbalance between the number of right-handed and left-handed fermions (a nice review can be found in Ref. [2]). The CME is thought to be responsible for charge asymmetries observed in heavy ion collisions at RHIC and LHC [3]. It also might play a role in the transport properties of advanced new materials, the so-called Weyl semi-metals in which the effective charge carriers can be modeled as 3 + 1 dimensional Dirac fermions [4].The CME is however only one representative of a whole class of anomaly related transport phenomena. A full classification of such phenomena has been obtained via Kubo formulas in [5]. It turned out that not only the usual axial or chiral anomalies give rise to dissipationless transport but that there is also a distinguished place for the axial gravitational anomaly.In general, anomaly related transport is sourced by either external magnetic fields or by vortices in the fluid * On leave from ITEP, Moscow, Russia.† Deceased. of chiral fermions [6]1 . Thus we can distinguish between chiral magnetic and chiral vortical effects. The gravitational anomaly comes in through the chiral vortical effect (CVE). Even in the absence of chemical potentials the gravitational anomaly gives rise to a chiral vortical effect at finite temperaturewhere J 5 is the axial current and ω = ∇× v is the vorticity of the fluid velocity v. In the absence of matter, the conductivitydepends on the temperature T and the gravitational anomaly coefficient. Equation (1) is valid for a theory consisting of massless fermions. In a basis of left-and right-handed Weyl fermions q l (q r ) are the charges of the l...