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Protection of effective hydrodynamics against Anderson localization in two dimensional nematic quantum criticality

We investigate effects of mutual correlations between hydrodynamic fluctuations and weak-localization corrections on Anderson localization, based on the renormalization group analysis up to the two-loop order. As a result, we find that the absence of quantum coherence in two-particle composite excitations gives rise to a novel disordered non-Fermi liquid metallic state near two-dimensional nematic quantum criticality with nonmagnetic disorders. This research would be the first step in understanding the T -linear electrical resistivity as a characteristic feature of non-Fermi liquids and the origin of unconventional superconductivity from effective hydrodynamics of quantum criticality.