Strong-disorder renormalization group for periodically driven systems

Abstract

Quenched randomness can lead to robust non-equilibrium phases of matter in periodically driven (Floquet) systems. Analyzing transitions between such dynamical phases requires a method capable of treating the twin complexities of disorder and discrete time-translation symmetry. We introduce a real-space renormalization group approach, asymptotically exact in the strong-disorder limit, and exemplify its use on the periodically driven interacting quantum Ising model. We analyze the universal physics near the critical lines and multicritical point of this model, and demonstrate the robustness of our results to the inclusion of weak interactions. arXiv:1807.09767v2 [cond-mat.dis-nn] 9 Nov 2018 with the following decimation rules:1234 tan Ω 45 , J 13 = J 13 − c J 24 U 1234 tan Ω 45 ,J 23 = cU 2345 , J 26 = J 24 J 56 tan Ω 45 + cU 2456 ,J 27 = J 24 J 57 tan Ω 45 + cU 2457 , J 36 = J 34 J 56 tan Ω 45 + cU 3456 ,J 37 = J 34 J 57 tan Ω 45 + cU 3457 , J 67 = −cU 6789 ,J 68 = J 68 − c J 57 U 5678 tan Ω 45 , J 78 = J 78 + c J 56 U 5678 tan Ω 45 ,J 89 = J 89 , J 9,10 = J 9,10 , U 0123 = U 0123 ,Ũ 1236 = J 56 U 1234 tan Ω 45 , U 1237 = J 57 U 1234 tan Ω 45 ,Ũ 2678 = J 24 U 5678 tan Ω 45 , U 3678 = J 34 U 5678 tan Ω 45 ,Ũ 689,10 = U 689,10 , U 789,10 = U 789,10 ,W 123678 = U 1234 U 5678 tan Ω 45 . * wberdanier@berkeley.edu 1 A. Eckardt, Rev. Mod. Phys. 89, 011004 (2017).

Discrete Time Crystals

“…(13), where J z is the mean value of the diordered interaction strength and = g − 1 is the π-pulse imperfection. For large the MBL discrete time crystal melts into a symmetry unbroken phase [15,82], while for large J z , the disorder is not strong enough to localize the system, leading to a thermal phase. (d) This qualitative phase diagram is directly observed in small system trapped ion experiments described in Section VI A.…”

Flow equations for disordered Floquet systems

“…Numerical approaches based on exact diagonalization of the full evolution operator allow access to the complete information of the Floquet eigenstates and eigenmodes, but are usually limited to very small system sizes. In the context of disordered systems, powerful methods such as the strong-disorder renormalization group have been extended to the Floquet context [52][53][54].…”

Activating critical exponent spectra with a slow drive

“…As a first result of this approach, we demonstrate that the structure of the adiabatic flow equations reduces the KZ hypothesis to the conventional scaling hypothesis: no independent information is encoded in them [27,34,35]. This is because a slow drive only affects the large-scale physics (conversely, a fast drive acts at small scales and can produce new critical exponents [36][37][38][39]). The most important new implication of our analysis is, however, based on the downshift of the spectrum of critical exponents (see Fig.…”