Floquet time crystals in clock models

Abstract

We construct a class of period-n-tupling discrete time crystals based on Zn clock variables, for all the integers n. We consider two classes of systems where this phenomenology occurs, disordered models with short-range interactions and fully connected models. In the case of short-range models we provide a complete classification of time-crystal phases for generic n. For the specific cases of n = 3 and n = 4 we study in details the dynamics by means of exact diagonalisation. In both cases, through an extensive analysis of the Floquet spectrum, we are able to fully map the phase diagram. In the case of infinite-range models, the mapping onto an effective bosonic Hamiltonian allows us to investigate the scaling to the thermodynamic limit. After a general discussion of the problem, we focus on n = 3 and n = 4, representative examples of the generic behaviour. Remarkably, for n = 4 we find clear evidence of a new crystal-to-crystal transition between period n-tupling and period n/2-tupling.

Real-time-dynamics quantum simulation of (1+1)-dimensional lattice QED with Rydberg atoms

“…Our quantum simulator is therefore a versatile and reliable experimental setup useful for investigating exotic properties of discrete and continuous Abelian lattice gauge theories [40,41]. Possible outlook for this work is the extension to two-dimensional theories, in continuity with a recent proposal about the study of 2D pure gauge systems [42], as well as the application of this protocol for simulating clock variables to different models such as time crystals [43,44].…”

Route to Extend the Lifetime of a Discrete Time Crystal in a Finite Spin Chain without Disorder

“…Intriguingly, recent research efforts have shown that it is possible to realize a robust DTC in the absence of disorder [40,41,[52][53][54][55][56]. This surprising observation implies the presence of mechanisms other than MBL that can prevent Floquet systems from heating up.…”

“…Furthermore, to qualify as a genuine non-equilibrium phase of matter, these sub-harmonic oscillations must persist at long times (t/T 1), without fine tuning the Hamiltonian parameters [40,41]. Through several theoretical and experimental studies, the existence of the DTC phase has now been firmly established [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56].…”

Generalized criteria of symmetry breaking. A strategy for quantum time crystals

“…Let us stress once more that, although most recent developments concerning the realization of quantum time crystals have mainly resorted to the introduction of a fine-tuned external periodic drive in the spirit of Floquet time crystals [9,4,15,12,16,17,18], we only consider models with timeindependent Hamiltonians.…”