Classical approaches to prethermal discrete time crystals in one, two, and three dimensions

Published on Sep 27, 2021in Physical Review B4.036
· DOI :10.1103/PHYSREVB.104.094308
Andrea Pizzi6
Estimated H-index: 6
(University of Cambridge),
Andreas Nunnenkamp30
Estimated H-index: 30
(University of Nottingham),
Johannes Knolle30
Estimated H-index: 30
(TUM: Technische Universität München)
Source
Abstract
We provide a comprehensive account of prethermal discrete time crystals within classical Hamiltonian dynamics, complementing and extending our recent work [Phys. Rev. Lett. 127, 140602 (2021)]. Considering power-law interacting spins on one-, two-, and three-dimensional hypercubic lattices, we investigate the interplay between dimensionality and interaction range in the stabilization of these non-equilibrium phases of matter that break the discrete time-translational symmetry of a periodic drive.
References45
Newest
#1Bingtian Ye (University of California, Berkeley)H-Index: 5
#2Francisco Machado (University of California, Berkeley)H-Index: 10
Last. Norman Y. Yao (University of California, Berkeley)H-Index: 46
view all 3 authors...
We demonstrate that the prethermal regime of periodically driven (Floquet), classical many-body systems can host nonequilibrium phases of matter. In particular, we show that there exists an effective Hamiltonian that captures the dynamics of ensembles of classical trajectories despite the breakdown of this description at the single trajectory level. In addition, we prove that the effective Hamiltonian can host emergent symmetries protected by the discrete time-translation symmetry of the drive. ...
Source
#1Andrea PizziH-Index: 6
#2Andreas NunnenkampH-Index: 30
Last. Johannes KnolleH-Index: 30
view all 3 authors...
Systems subject to a high-frequency drive can spend an exponentially long time in a prethermal regime, in which novel phases of matter with no equilibrium counterpart can be realized. Due to the notorious computational challenges of quantum many-body systems, numerical investigations in this direction have remained limited to one spatial dimension, in which long-range interactions have been proven a necessity. Here, we show that prethermal non-equilibrium phases of matter are not restricted to t...
#1Muath NatshehH-Index: 2
#2Andrea GambassiH-Index: 38
Last. Aditi MitraH-Index: 28
view all 3 authors...
The critical properties characterizing the formation of the Floquet time crystal in the prethermal phase are investigated analytically in the periodically driven O(N)model. In particular, we focus on the critical line separating the trivial phase with period synchronized dynamics and absence of long-range spatial order from the non-trivial phase where long-range spatial order is accompanied by period-doubling dynamics. In the vicinity of the critical line, with a combination of dimensional ex...
Source
We study correlations, transport and chaos in a Heisenberg magnet as a classical model many-body system. By varying temperature and dimensionality, we can tune between settings with and without symmetry breaking and accompanying collective modes or quasiparticles. We analyse both conventional and out-of-time-ordered spin correlators (`decorrelators') to track the spreading of a spatiotemporally localised perturbation -- the wingbeat of the butterfly -- as well as transport coefficients and Lyapu...
Source
#1Andrea Pizzi (University of Cambridge)H-Index: 6
#2Johannes Knolle (Imperial College London)H-Index: 30
Last. Andreas Nunnenkamp (University of Nottingham)H-Index: 30
view all 3 authors...
Discrete time crystals are periodically driven systems characterized by a response with periodicity nT, with T the period of the drive and n > 1. Typically, n is an integer and bounded from above by the dimension of the local (or single particle) Hilbert space, the most prominent example being spin-1/2 systems with n restricted to 2. Here, we show that a clean spin-1/2 system in the presence of long-range interactions and transverse field can sustain a huge variety of different ‘higher-order’ di...
Source
#1Andrea Pizzi (University of Cambridge)H-Index: 6
#2Andreas Nunnenkamp (University of Nottingham)H-Index: 30
Last. Johannes Knolle (Imperial College London)H-Index: 30
view all 3 authors...
Stochastic processes govern the time evolution of a huge variety of realistic systems throughout the sciences. A minimal description of noisy many-particle systems within a Markovian picture and with a notion of spatial dimension is given by probabilistic cellular automata, which typically feature time-independent and short-ranged update rules. Here, we propose a simple cellular automaton with power-law interactions that gives rise to a bistable phase of long-ranged directed percolation whose lo...
Source
#1Daniel Malz (MPG: Max Planck Society)H-Index: 12
#2Andrea Pizzi (University of Cambridge)H-Index: 6
Last. Johannes Knolle (Imperial College London)H-Index: 30
view all 4 authors...
The authors explore a model of seasonal epidemic spreading and show that it displays a time-crystalline phase with characteristic subharmonic response.
Source
#1Hongzheng ZhaoH-Index: 5
#2Florian MintertH-Index: 36
Last. Johannes KnolleH-Index: 30
view all 4 authors...
We study heating in interacting quantum many-body systems driven by random sequences with n-ultipolar correlations, corresponding to a polynomially suppressed low frequency spectrum. For n\geq 1 we find a prethermal regime, the lifetime of which grows algebraically with the driving rate, with exponent {2n+1} A simple theory based on Fermi's golden rule accounts for this behaviour. The quasiperiodic Thue-Morse sequence corresponds to the n\to \inftylimit, and accordingly exhibits an e...
Source
#1Muath NatshehH-Index: 2
#2Andrea GambassiH-Index: 38
Last. Aditi MitraH-Index: 28
view all 3 authors...
The periodically driven O(N) model is studied near the critical line separating a disordered paramagnetic phase from a period doubled phase, the latter being an example of a Floquet time crystal. The time evolution of one-point and two-point correlation functions are obtained within the Gaussian approximation and perturbatively in the drive amplitude. The correlations are found to show not only period doubling, but also power-law decays at large spatial distances. These features are compared wit...
Source
#1David J. Luitz (MPG: Max Planck Society)H-Index: 24
#2Roderich Moessner (MPG: Max Planck Society)H-Index: 73
Last. Vedika Khemani (Stanford University)H-Index: 27
view all 4 authors...
Optimal application of a magnetic field can increase the lifetime of transient time crystals by orders of magnitude, and autocorrelation functions can distinguish transient time crystals from infinitely long-lived ones.
Source
Cited By3
Newest
#1Reyhaneh Khasseh (MPG: Max Planck Society)H-Index: 3
Source
#1Bingtian Ye (University of California, Berkeley)H-Index: 5
#2Francisco Machado (University of California, Berkeley)H-Index: 10
Last. Norman Y. Yao (University of California, Berkeley)H-Index: 46
view all 3 authors...
We demonstrate that the prethermal regime of periodically driven (Floquet), classical many-body systems can host nonequilibrium phases of matter. In particular, we show that there exists an effective Hamiltonian that captures the dynamics of ensembles of classical trajectories despite the breakdown of this description at the single trajectory level. In addition, we prove that the effective Hamiltonian can host emergent symmetries protected by the discrete time-translation symmetry of the drive. ...
Source
#1Andrea PizziH-Index: 6
#2Andreas NunnenkampH-Index: 30
Last. Johannes KnolleH-Index: 30
view all 3 authors...
Systems subject to a high-frequency drive can spend an exponentially long time in a prethermal regime, in which novel phases of matter with no equilibrium counterpart can be realized. Due to the notorious computational challenges of quantum many-body systems, numerical investigations in this direction have remained limited to one spatial dimension, in which long-range interactions have been proven a necessity. Here, we show that prethermal non-equilibrium phases of matter are not restricted to t...
Source
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