Semisuper Efimov Effect of Two-Dimensional Bosons at a Three-Body Resonance

Han Guangze

Yusuke Horinouchi

We study the semisuper-Efimov effect, which is found for four identical bosons with a resonant three-body interaction in 2D, in various systems. Based on solutions of bound-state and renormalization-group equations, we first demonstrate an emergence of the semisuper-Efimov effect in mass-imbalanced bosons in 2D. Compared with the Efimov and the super-Efimov effects, the mass ratio-dependent scaling parameter is unexpectedly found to take on a finite value even for extremely mass-imbalanced situations, where the mass ratio is 0 or $\infty$. By a renormalization-group analysis, we also show that a weak two-body interaction sustains the semisuper-Efimov effect. Finally, we liberate the universality of the semisuper-Efimov effect from 2D by showing that bosons with linear-dispersion relation support the semisuper-Efimov effect in 1D.

Yusuke Nishida

Wave-particle duality in quantum mechanics allows for a halo bound state whose spatial extension far exceeds a range of the interaction potential. What is even more striking is that such quantum halos can be arbitrarily large on special occasions. The two examples known so far are the Efimov effect and the super Efimov effect, which predict that spatial extensions of higher excited states grow exponentially and double exponentially, respectively. Here, we establish yet another new class of arbitrarily large quantum halos formed by spinless bosons with short-range interactions in two dimensions. When the two-body interaction is absent but the three-body interaction is resonant, four bosons exhibit an infinite tower of bound states whose spatial extensions scale as R_{n}∼e^{(πn)^{2}/27} for a large n. The emergent scaling law is universal and is termed a semisuper Efimov effect, which together with the Efimov and super Efimov effects constitutes a trio of few-body universality classes allowing for arbitrarily large quantum halos.

Qingze Guan, D. Blume

Yusuke Nishida

Exchange of the resonant pair of fermions between two bosons is shown to induce a nearly scale-invariant attraction, which leads to an infinite number of bound states obeying the universal scaling law of binding energies. This system constitutes a new member in the class of semisuper Efimov effect, potentially relevant to two-neutron halo nuclei as well as ultracold atoms.

Orest Hryhorchak, V. Pastukhov