Universal Properties of the Four-Boson System in Two Dimensions

TL;DR

This paper investigates the universal properties of four-boson systems in two dimensions with short-range attraction, revealing two bound states with energies proportional to the two-body binding energy, independent of interaction details.

Contribution

It provides the first precise calculation of four-boson binding energies in 2D, demonstrating universality and identifying exactly two bound states.

Findings

Two bound states identified: ground and excited.

Binding energies are proportional to the two-body binding energy.

Results support universality in 2D four-boson systems.

Abstract

We consider the nonrelativistic four-boson system in two dimensions interacting via a short-range attractive potential. For a weakly attractive potential with one shallow two-body bound state with binding energy B_2, the binding energies B_N of shallow N-body bound states are universal and thus do not depend on the details of the interaction potential. We compute the four-body binding energies in an effective quantum mechanics approach. There are exactly two bound states: the ground state with B_4^(0)=197.3(1)B_2 and one excited state with B_4^(1)=25.5(1)B_2. We compare our results to recent predictions for N-body bound states with large N>>1.