Lack of a genuine time crystal in a chiral soliton model

TL;DR

This paper refutes a recent claim that a genuine time crystal can exist in a chiral soliton model, demonstrating that the lowest energy state does not exhibit periodic motion and thus is not a true time crystal.

Contribution

The authors provide a counterexample showing the absence of genuine time crystals in the considered model, challenging prior claims of their existence.

Findings

The lowest energy state lacks periodic motion.

The proposed solution has lower energy without time crystal behavior.

The claim of a genuine time crystal in this model is incorrect.

Abstract

In a recent publication [Phys. Rev. Lett. {\bf 124}, 178902] \"Ohberg and Wright claim that in a chiral soliton model it is possible to realize a genuine time crystal which corresponds to a periodic evolution of an inhomogeneous probability density in the lowest energy state. We show that this result is incorrect and present a solution which possesses lower energy with the corresponding probability density that does not reveal any motion. It implies that the authors' conclusion that a genuine time crystal can exist in the system they consider is not true.