Lack of a genuine time crystal in a chiral soliton model

Abstract

In a recent publication [Phys. Rev. Lett. 124, 178902 (2020)PRLTAO0031-900710.1103/PhysRevLett.124.178902], Öhberg 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.