We study the mesoscopic fluctuations and correlations of the local density of states near metal-insulator transitions in disordered interacting electronic systems. We show that the multifractal behavior of the local density of states survives in the presence of Coulomb
interaction. We calculate the spectrum of multifractal exponents in $2+\epsilon$ spatial dimensions for symmetry classes characterized by broken (partially or fully) spin-rotation invariance and show that it differs from that in the absence of interaction. We also estimate the multifractal exponents at the Anderson metal-insulator transition in 2D systems with preserved spin-rotation invariance. Our results for multifractal correlations of the local density of states are in qualitative agreement with recent experimental findings. The results are published in Refs. [1,2,3].

[1] I.S. Burmistrov, I.V. Gornyi, A.D. Mirlin, Phys. Rev. Lett. 111, 066601 (2013).
[2] I.S. Burmistrov, I.V. Gornyi, A.D. Mirlin, Phys. Rev. B 89, 035430 (2014).
[3] I.S. Burmistrov, I.V. Gornyi, A.D. Mirlin, Phys. Rev. B 91, 085427 (2015).