Recent experiments in ultraclean semiconductor quantum wells show indisputable evidence of the breakdown of the conventional Fermi liquid at low electron densities [1-3]. Apart from the formation of the correlated insulating phases , the metallic precursor phase shows large viscosity of the electron liquid with the linear in temperature resistivity , the properties that are typical to so-called strange metals or non-Fermi liquids. Exceptionally high quality of the devices [1-3] rules out the effects of disorder shifting the responsibility to the electron-electron interaction. The perturbative treatment such as the Hartree-Fock and the random phase approximations fail to fit the experimental data and the non-perturbative approach has to be developed instead. Here we suggest the non-perturbative analytical approach that is based on the dimensional reduction allowing us to reduce the number of spatial dimensions D > 1 of the D-dimensional interacting electron gas to a single effective spatial dimension. We find that the low-energy physics close to the Fermi surface is governed by the emergent conformal symmetry that allows us to find the exact asymptotic forms of the electron Green function, dressed interaction and the linear response functions. This approach allows us to describe the metallic non-Fermi-liquid state of the interacting electron gas in D > 1 spatial dimensions. Trying this non-Fermi-liquid state against various instabilities could pave the way for understanding the insulating phases observed in the ultraclean low-density quantum wells.
 M. S. Hossain et al., https://doi.org/10.1073/pnas.2018248117
 M. S. Hossain et al., PRL 127, 116601 (2021)
 A. C. Keser et al., PRX 11, 031030 (2021)