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In a recent paper (Phys. Rev. Lett. 123, 210602), Kozin and Kyriienko claim to realize genuine ground state time crystals by studying models with long-ranged and infinite-body interactions. Here we point out that their models are doubly problematic: they are unrealizable ${it and}$ they violate well established principles for defining phases of matter. Indeed with infinite body operators allowed, almost all quantum systems are time crystals. In addition, one of their models is highly unstable and another amounts to isolating, via fine tuning, a single degree of freedom in a many body system--allowing for this elevates the pendulum of Galileo and Huygens to a genuine time crystal.
In the note by Khemani et al. [arXiv:2001.11037] the authors express conceptual disagreement with our recent paper on quantum time crystals [Phys. Rev. Lett. 123, 210602]. They criticise the idealized nature of the considered quantum time crystal, an
Time crystals correspond to a phase of matter where time-translational symmetry (TTS) is broken. Up to date, they are well studied in open quantum systems, where external drive allows to break discrete TTS, ultimately leading to Floquet time crystals
We propose and analyze a generalization of the Kitaev chain for fermions with long-range $p$-wave pairing, which decays with distance as a power-law with exponent $alpha$. Using the integrability of the model, we demonstrate the existence of two type
Spin ensembles coupled to optical cavities provide a powerful platform for engineering synthetic quantum matter. Recently, we demonstrated that cavity mediated infinite range interactions can induce fast scrambling in a Heisenberg $XXZ$ spin chain (P
We study the eigenstate properties of a nonintegrable spin chain that was recently realized experimentally in a Rydberg-atom quantum simulator. In the experiment, long-lived coherent many-body oscillations were observed only when the system was initi