# Semisuper Efimov effect of two-dimensional bosons at a three-body resonance

## TL;DR

This paper introduces a new universal quantum halo phenomenon called the semisuper Efimov effect, where four two-dimensional bosons form an infinite tower of bound states with super-exponentially increasing size under specific three-body resonance conditions.

## Contribution

The paper discovers the semisuper Efimov effect, a novel class of arbitrarily large quantum halos in 2D bosons with resonant three-body interactions, expanding the universality classes of few-body quantum phenomena.

## Key findings

- Identifies the semisuper Efimov effect with a unique scaling law.
- Shows the effect occurs when two-body interactions are absent but three-body interactions are resonant.
- Provides a universal scaling law for the size of bound states, R_n ~ e^{(\pi n)^2/27}.

## Abstract

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 $R_n\sim e^{(\pi n)^2/27}$ 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.