Multifractality and electron-electron interaction at Anderson transitions

摘要

Mesoscopic fluctuations and correlations of the local density of states arestudied near metal-insulator transitions in disordered interacting electronicsystems. We show that the multifractal behavior of the local density of statessurvives in the presence of Coulomb interaction. We calculate the spectrum ofmultifractal exponents in $2+\epsilon$ spatial dimensions for symmetry classescharacterized by broken (partially or fully) spin-rotation invariance and showthat it differs from that in the absence of interaction. We also estimate themultifractal exponents at the Anderson metal-insulator transition in 2D systemswith preserved spin-rotation invariance. Our results for multifractalcorrelations of the local density of states are in qualitative agreement withrecent experimental findings.