A comment on "Discrete time crystals: rigidity, criticality, and realizations"

TL;DR

This paper critically examines existing models claiming to realize many-body localized discrete time crystals, demonstrating that these models do not exhibit true MBL DTC behavior within the specified parameters and clarifying the nature of observed oscillations.

Contribution

The authors provide a rigorous analysis showing that previously proposed models do not support genuine MBL DTC phases, challenging prior claims and interpretations.

Findings

Models show rapid decay of oscillations, not robust period doubling.

Long-lived oscillations are due to static low-temperature physics, not MBL DTC.

Absence of MBL DTC in the analyzed long-range trapped ion model.

Abstract

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].