Discrete time crystals in many-body quantum chaos

Abstract

Discrete time crystals (DTCs) are new phases of matter characterized by the presence of an observable evolving with nT periodicity under a T -periodic Hamiltonian, where n > 1 is an integer insensitive to small parameter variations. In particular, DTCs with n = 2 have been extensively studied in periodically quenched and kicked spin systems in recent years. In this paper, we study the emergence of DTCs from the many-body quantum chaos perspective, using a rather simple model depicting a harmonically driven spin chain. We advocate to first employ a semiclassical approximation to arrive at a mean-field Hamiltonian and then identify the parameter regime at which DTCs exist, with standard tools borrowed from studies of classical chaos. Specifically, we seek symmetric-breaking solutions by examining the stable islands on the Poincaré surface of section of the mean-field Hamiltonian. We then turn to the actual many-body quantum system, evaluate the stroboscopic dynamics of the total magnetization in the full quantum limit, and verify the existence of DTCs. Our effective and straightforward approach indicates that in general DTCs are one natural aspect of many-body quantum chaos with mixed classical phase space structure.Our approach can also be applied to general time-periodic systems, which is thus promising for finding DTCs with n > 2 and opening possibilities for exploring DTCs properties beyond their time-translational breaking features.

Floquet time crystals in driven spin systems with all-to-all $p$-body interactions

“…Our work significantly expands previous studies on mean-field FTC phases in spin systems with infinite range two-body interactions [9,19,20], a scenario which naturally leads to lack of ergodicity even in clean systems without disorder or many-body localization. In particular, Ref.…”

“…III A). This is in fact the method employed in [20] and [19] for the identification of higher period FTC phases, which we have put into a more formal footing. However, the emergent symmetry discussed above is a feature of only a region of phase space in the vicinity of the y − z plane.…”

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

“…Eventually however, the existence of quantum time crystals in equilibrium was ruled out by a no-go theorem [8]. This crucial insight has prompted several researchers to explore the possibility of realizing time crystals in non-equilibrium quantum systems [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. These efforts have been immensely fruitful and led to the development of an active area of research [27][28][29][30][31][32][33][34][35][36][37][38][39].…”

Quantum repetition codes as building blocks of large-period discrete time crystals

“…The possibility for local spin-1/2 systems to yield larger period DTCs was previously envisioned by our previous study [19] of a continuously driven spin chain through extensive numerics under semiclassical approximation. Such larger period DTCs were however only * Raditya.Bomantara@sydney.edu.au expected to arise at sufficiently large system sizes and under very specific choice of initial states.…”