The Harper equation arising out of a tight-binding model of electrons on a honeycomb lattice subject to a uniform magnetic field perpendicular to the plane is studied. Contrasting and complementary approaches involving von Neumann entropy, fidelity, fidelity susceptibility, and multifractal analysis are employed to characterize the phase diagram. Remarkably even in the absence of the quasi-periodic on-site potential term, the Hamiltonian allows for a metal-insulator transition. The phase diagram consists of three phases: two metallic phases and an insulating phase. A variant model where next nearest neighbor hopping is included, exhibits a mobility edge and does not allow for a simple single phase diagram characterizing all the eigenstates.

An efficient microwave-assisted protocol for the synthesis of fluorinated coumarino sulfonamides 3 was achieved. First the fluoro arylamines were reacted with methyl 2-chlorosulfonyl acetate to afford compounds 2 followed by Knoevenagel condensation with substituted salicylaldehydes to give fluorinated coumarino sulfonamides 3. Comparison of conventional and microwave irradiation showed the later procedure required shorter reaction times, generally gave higher yields and was applicable to a larger set of substrates.

We study the effect of short range interactions in three dimensional nodal-line semimetals with linear band crossings. We analyze the Yukawa theories for gapped instabilities in the charge, spin and superconducting channels using the Wilsonian renormalization group framework, employing a large number of fermion flavors N f for analytical control. We obtain stable non-trivial fixed points and provide a unified description of the critical exponents for the ordering transitions in terms of the number of order parameter components N b systematically to order 1/N f . We show that in all cases, the dynamical exponent z = 1 in one loop, whereas 1/N f corrections to various exponents follow from the anomalous dimension of the bosonic fields only.

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