Higher period Floquet time crystals stabilized by multi-body interactions
April 12, 2022 - Manuel H. Muñoz-Arias, Karthik Chinni, and Pablo M. Poggi
Figure 1. Illustration of the emergence of a period-three Floquet time crystal phase in a periodically driven quantum p-spin model.
Out-of-equilibrium phases of matter represent a natural generalization of critical phenomena and quantum phase transitions to quantum systems far from equilibrium, and even in presence of an external driving. A paradigmatic example are the Floquet time crystals, which emerge in periodically driven systems in absence of any dissipation or decoherence. Under the action of a periodic drive, the system possesses a discrete time-translation symmetry, as the Hamiltonian is invariant under time displacements by a unit equal to the period T of the external drive. In a Floquet time crystal, this symmetry is spontaneous broken as generic macroscopic observables exhibit stable oscillations at a period which is an integer multiple of the period of the drive nT.
In a recent work from CQuIC  led by graduate student Manuel Muñoz-Arias together with Karthik Chinni and Pablo Poggi, the authors show the emergence of such time crystal phases for spin systems which interact with all-to-all multi-body interactions. The mean-field limit of these type of models can be elegantly described in terms of the motion of a classical ‘top’ on a spherical phase space, which allows the authors to develop comprehensive theory for mean-field Floquet time crystal phases by borrowing results from the theory of dynamical systems. Using this theory, it is shown that increasing the degree of multi-body interaction allows to access novel, higher-order multiplexed Floquet time crystal, which had been proven hard to find with usual two-body interactions. Furthermore, this theory allows to show that the emergence of these phases of matter can be mapped to certain types of quantum phase transitions in the excited states, where a constant portion of the eigenstates undergo a so-called excited state quantum phase transition, which leads to a sharp transformation of their macroscopic structural properties. As a consequence of this, the dynamical response of the system also undergoes a drastic change, which can in turn be characterized as dynamical quantum phase transition.
This study establishes a route to access and control novel Floquet time crystals phases and also provides fundamental connections with known phenomenology of excited and dynamical phase transitions, thus helping move forward our understanding of out-of-equilibrium phases of matter. This work was published in Physical Review Research and can be accessed at the following link: https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.4.023018
 Manuel H. Muñoz-Arias, Karthik Chinni, and Pablo M. Poggi, Phys. Rev. Research 4, 023018 (2022).