Quantum collapse in three and two dimensions (3D and 2D) is induced by attractive potential $\sim -r^{-2}$. It was demonstrated that the mean-field (MF) cubic self-repulsion in the 3D bosonic gas suppresses the collapse and creates the missing ground state (GS). However, the cubic nonlinearity is not strong enough to suppress the 2D collapse. We demonstrate that the Lee-Hung-Yang (LHY) quartic term, induced by quantum fluctuations around the MF state, is sufficient for the stabilization of the 2D gas against the collapse. By means of 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 wave function at small and large distances from the center and the Thomas-Fermi approximation, we construct stable GS, with a singular density $\sim r^{-4/3}$ but convergent integral norm. Counterintuitively, the stable GS exists even if the external potential is repulsive, with the strength falling below a certain critical value. An explanation to this finding is given. Along with the GS, singular vortex states are produced too, and their stability boundary is found analytically. Unstable vortices spontaneously transform into the stable GS, expelling the vorticity to the periphery.

中文翻译：

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Lee-Huang-Yang效应对吸引场中准二维量子坍塌的抑制

引力诱使3维和2维（3D和2D）量子崩溃 $〜-{\mathrm{[R}}^{-2}$。事实证明，3D硼气体中的平均场（MF）立方自排斥抑制了塌陷并产生了缺失的基态（GS）。但是，立方非线性不足以抑制2D塌陷。我们证明，由MF状态周围的量子涨落引起的Lee-Hung-Yang（LHY）四次项足以稳定2D气体以防止崩溃。通过包括LHY项在内的Gross-Pitaevskii方程的数值解，并借助分析方法，例如在距中心较小和较大距离处的波动函数展开和Thomas-Fermi逼近，我们构造了稳定的GS，具有奇异密度$〜{\mathrm{[R}}^{-4/3}$但是收敛的积分范数。与直觉相反，即使外部电势是排斥的，也存在稳定的GS，其强度下降到某个临界值以下。对此发现给出了解释。与GS一起，也产生了奇异的涡态，并通过分析找到了它们的稳定性边界。不稳定的涡流自发地转变为稳定的GS，从而将涡流推向外围。