Abstract We analyze a variety of integration schemes for the momentum space functional renormalization group calculation with goal finding an optimized scheme. Using square lattice $$t-t'$$ t - ′ Hubbard model as testbed we define...

Band gap modification for small-diameter (approximately 1 nm) silicon nanowires resulting from the use of different species for surface termination is investigated by density functional theory calculations. Because of quantum confinement, small-diameter wires exhibit a direct band gap that increases as the wire diameter narrows, irrespective of surface termination. This effect has been observed...

Interactions growing slower than a certain exponential of the square scalar field are well behaved when evolved under functional renormalization group linearized around Gaussian fixed point. They satisfy properties usually taken for granted, and reproduce standard perturbative quantization. However, more challenging effects appear, interactions grow faster this. We show explicitly that firstly,...