  The Letter by N. Y. Yao et. al. [1,2] presents three models for realizing a
many-body localized discrete time-crystal (MBL DTC): a short-ranged model [1],
its revised version [2], as well as a long-range model of a trapped ion
experiment [1,3]. We show that none of these realize an MBL DTC for the
parameter ranges quoted in Refs. [1,2]. The central phase diagrams in [1]
therefore cannot be reproduced. The models show rapid decay of oscillations
from generic initial states, in sharp contrast to the robust period doubling
dynamics characteristic of an MBL DTC. Long-lived oscillations from special
initial states (such as polarized states) can be understood from the familiar
low-temperature physics of a static transverse field Ising model, rather than
the nonequilibrium physics of an eigenstate-ordered MBL DTC. Our results on the
long-range model also demonstrate, by extension, the absence of an MBL DTC in
the trapped ion experiment of Ref. [3].
