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Quantum collapse in three and two dimensions (3D and 2D) is induced byattractive potential ~ -1/r^2. It was demonstrated that the mean-field (MF)cubic self-repulsion in the 3D bosonic gas suppresses the collapse and createsthe missing ground state (GS). However, the cubic nonlinearity is not strongenough to suppress the 2D collapse. We demonstrate that the Lee-Hung-Yang (LHY)quartic term, induced by quantum fluctuations around the MF state, issufficient for the stabilization of the 2D gas against the collapse. By meansof numerical solution of the Gross-Pitaevskii equation including the LHY term,as well as with the help of analytical methods, such as expansions of the wavefunction at small and large distances from the center and the Thomas-Fermiapproximation, we construct stable GS, with a singular density, ~ 1/r^{4/3},but convergent integral norm. Counter-intuitively, the stable GS exists even ifthe external potential is repulsive, with the strength falling below a certaincritical value. An explanation to this finding is given. Along with the GS,singular vortex states are produced too, and their stability boundary is foundanalytically. Unstable vortices spontaneously transform into the stable GS,expelling the vorticity to periphery.

Suppression of the quasi-two-dimensional quantum collapse in the attraction field by the Lee-Huang-Yang effect