A structure of periodically ordered atoms in space which is stable to external perturbation is called a crystalline structure. These structures have a repeating pattern in space and remains unchanged as time passes. Different kinds of this structure like photonic crystals and cold atom lattices are applicable in different areas of science. The idea of space-time crystal in which the structure is ordered both in space and time was proposed by Frank Wilczek in 2012. The importance of time translational symmetry that noticed in this kind of crystal is that it underlies reproducibility of the crystal and conservation of energy. Naturally oscillating physical systems (as one of the simplest repeating patterns in time) exists in very large numbers but all of them require an input energy to drive. The idea behind a crystal in time domain was that it requires no energy input. So the main question behind the idea of time crystal is: “whether time-translation symmetry might be spontaneously broken in a closed quantum mechanical system?” In response to this question several articles were published in 2013 claiming to show that ground-state space-time crystals cannot be realized in the simple setting and are ruled out by the no-go theorem.
According to this theorem, quantum time crystals in equilibrium are not possible. On the other hand, in open quantum systems where an external drive is allowed to break the time translational symmetry, time crystals are well studied. But perhaps the most important aspect of the time-crystal notion is that it envisages broken time-translation symmetry as an equilibrium phenomenon, rather than a non-equilibrium response to a driving force.
In the current paper the authors studied a closed system to investigate this aspect. They considered a spin-1/2 many-body Hamiltonian with long-range multi-spin interactions in the form of spin strings and showed that the unitary dynamics exhibits the time crystalline behavior and breaks continuous time translational symmetry. They showed that the proposed quantum time crystals are stable to local perturbations at zero temperature. Also, they revealed an intrinsic connection between continuous and discrete time translational symmetry.