Generalized Efimov effect in one dimension

TL;DR

This paper investigates a one-dimensional quantum system where two particles interact with a third via a scale-invariant inverse square potential, revealing a generalized Efimov effect characterized by a geometric series of bound states above a critical mass ratio.

Contribution

It demonstrates the occurrence of the generalized Efimov effect in a one-dimensional setting with inverse square interactions, extending Efimov physics beyond three dimensions.

Findings

Existence of a critical mass ratio for the Efimov effect

Emergence of a geometric series of three-body bound states

Discrete scale invariance in the system

Abstract

We study a one-dimensional quantum problem of two particles interacting with a third one via a scale-invariant subcritically attractive inverse square potential, which can be realized, for example, in a mixture of dipoles and charges confined to one dimension. We find that above a critical mass ratio, this version of the Calogero problem exhibits the generalized Efimov effect, the emergence of discrete scale invariance manifested by a geometric series of three-body bound states with an accumulation point at zero energy.