On the Efimov Effect for Four Particles in Dimension Two

TL;DR

This paper demonstrates that four particles in two dimensions with only three-body interactions can have infinitely many bound states, revealing an Efimov-like effect in this specific quantum system.

Contribution

It establishes the existence of an Efimov effect for four particles in two dimensions with short-range three-body forces, under the condition of virtual levels at zero energy.

Findings

Infinitely many bound states can exist in the specified system.

The Efimov effect extends to four particles in two dimensions with three-body interactions.

The result applies when each three-body subsystem has a virtual level at zero energy.

Abstract

We prove that the Schr\"odinger operator describing four particles in two dimensions, interacting solely through short-range three-body forces, can possess infinitely many bound states. This holds under the assumption that each three-body subsystem has a virtual level at zero energy. Our result establishes an analog of the Efimov effect for such four-particle systems in two dimensions.