skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

This content will become publicly available on February 10, 2021

Title: Classical discrete time crystals

Abstract

The spontaneous breaking of time-translation symmetry in periodically driven quantum systems leads to a new phase of matter: the discrete time crystal (DTC). This phase exhibits collective subharmonic oscillations that depend upon an interplay of non-equilibrium driving, many-body interactions and the breakdown of ergodicity. However, subharmonic responses are also a well-known feature of classical dynamical systems ranging from predator–prey models to Faraday waves and a.c.-driven charge density waves. This raises the question of whether these classical phenomena display the same rigidity characteristic of a quantum DTC. In this work, we explore this question in the context of periodically driven Hamiltonian dynamics coupled to a finite-temperature bath, which provides both friction and, crucially, noise. Focusing on one-dimensional chains, where in equilibrium any transition would be forbidden at finite temperature, we provide evidence that the combination of noise and interactions drives a sharp, first-order dynamical phase transition between a discrete time-translation invariant phase and an activated classical discrete time crystal (CDTC) in which time-translation symmetry is broken out to exponentially long timescales. Power-law correlations are present along a first-order line, which terminates at a critical point. We analyse the transition by mapping it to the locked-to-sliding transition of a d.c.-driven charge densitymore » wave. To conclude, building upon results from the field of probabilistic cellular automata, we conjecture the existence of classical time crystals with true long-range order, where time-translation symmetry is broken out to infinite times.« less

Authors:
ORCiD logo [1];  [2];  [3];  [4]
  1. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  2. Microsoft Research, Santa Barbara, CA (United States)
  3. Univ. of California, Santa Barabara, CA (United States)
  4. Princeton Univ., NJ (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC); National Science Foundation (NSF); US Army Research Office (ARO); USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1603622
Grant/Contract Number:  
[AC02-05CH11231; PHY-1654740; W911NF-17-1-0606; DMR1506119]
Resource Type:
Accepted Manuscript
Journal Name:
Nature Physics
Additional Journal Information:
[Journal Name: Nature Physics]; Journal ID: ISSN 1745-2473
Publisher:
Nature Publishing Group (NPG)
Country of Publication:
United States
Language:
English
Subject:
phase transitions and critical phenomena; quantum simulation; statistical physics

Citation Formats

Yao, Norman Y., Nayak, Chetan, Balents, Leon, and Zaletel, Michael P. Classical discrete time crystals. United States: N. p., 2020. Web. doi:10.1038/s41567-019-0782-3.
Yao, Norman Y., Nayak, Chetan, Balents, Leon, & Zaletel, Michael P. Classical discrete time crystals. United States. doi:10.1038/s41567-019-0782-3.
Yao, Norman Y., Nayak, Chetan, Balents, Leon, and Zaletel, Michael P. Mon . "Classical discrete time crystals". United States. doi:10.1038/s41567-019-0782-3.
@article{osti_1603622,
title = {Classical discrete time crystals},
author = {Yao, Norman Y. and Nayak, Chetan and Balents, Leon and Zaletel, Michael P.},
abstractNote = {The spontaneous breaking of time-translation symmetry in periodically driven quantum systems leads to a new phase of matter: the discrete time crystal (DTC). This phase exhibits collective subharmonic oscillations that depend upon an interplay of non-equilibrium driving, many-body interactions and the breakdown of ergodicity. However, subharmonic responses are also a well-known feature of classical dynamical systems ranging from predator–prey models to Faraday waves and a.c.-driven charge density waves. This raises the question of whether these classical phenomena display the same rigidity characteristic of a quantum DTC. In this work, we explore this question in the context of periodically driven Hamiltonian dynamics coupled to a finite-temperature bath, which provides both friction and, crucially, noise. Focusing on one-dimensional chains, where in equilibrium any transition would be forbidden at finite temperature, we provide evidence that the combination of noise and interactions drives a sharp, first-order dynamical phase transition between a discrete time-translation invariant phase and an activated classical discrete time crystal (CDTC) in which time-translation symmetry is broken out to exponentially long timescales. Power-law correlations are present along a first-order line, which terminates at a critical point. We analyse the transition by mapping it to the locked-to-sliding transition of a d.c.-driven charge density wave. To conclude, building upon results from the field of probabilistic cellular automata, we conjecture the existence of classical time crystals with true long-range order, where time-translation symmetry is broken out to infinite times.},
doi = {10.1038/s41567-019-0782-3},
journal = {Nature Physics},
number = ,
volume = ,
place = {United States},
year = {2020},
month = {2}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on February 10, 2021
Publisher's Version of Record

Save / Share:

Works referenced in this record:

Frequency Demultiplication
journal, September 1927

  • Van Der Pol, Balth; Van Der Mark, J.
  • Nature, Vol. 120, Issue 3019
  • DOI: 10.1038/120363a0

Simple mathematical models with very complicated dynamics
journal, June 1976


Pattern formation outside of equilibrium
journal, July 1993


Subharmonic Shapiro Steps and Devil's-Staircase Behavior in Driven Charge-Density-Wave Systems
journal, June 1984


Subharmonic Entrainment of Unstable Period Orbits and Generalized Synchronization
journal, October 1997


Period Doubling and Chaotic Behavior in a Driven Anharmonic Oscillator
journal, November 1981


Periodic entrainment of chaotic logistic map dynamics
journal, September 1990


LXXXVIII. On “relaxation-oscillations”
journal, November 1926

  • van der Pol, Balth.
  • The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 2, Issue 11
  • DOI: 10.1080/14786442608564127

Nonequilibrium first-order phase transition in coupled oscillator systems with inertia and noise
journal, February 2014


Harmonic and subharmonic shapiro steps in orthorhombic Tas3
journal, April 1985


Dynamics of driven charge-density waves: Subharmonic Shapiro steps with devil's staircase structure
journal, May 1985


Complete charge density-wave mode locking and freeze-out of fluctuations in NbSe 3
journal, October 1985


Noise tolerance of frequency-locked dynamics
journal, August 1987


Temporal coherence in the sliding charge-density-wave condensate
journal, October 1987


Unlocking mechanism in the ac dynamics of the Frenkel-Kontorova model
journal, September 1993


Temporal Order in Dirty Driven Periodic Media
journal, December 1995


Noise effects in the ac-driven Frenkel-Kontorova model
journal, March 2009


Subharmonic Shapiro steps in Josephson-junction arrays
journal, July 1991


Fractional Shapiro steps in ladder Josephson arrays
journal, June 1992


Quantum Time Crystals
journal, October 2012


Classical Time Crystals
journal, October 2012


Impossibility of Spontaneously Rotating Time Crystals: A No-Go Theorem
journal, August 2013


Time crystals: Can diamagnetic currents drive a charge density wave into rotation?
journal, September 2013


Modeling spontaneous breaking of time-translation symmetry
journal, March 2015


Absence of Quantum Time Crystals
journal, June 2015


Ideal mean-field transition in a modulated cold atom system
journal, September 2010


Dynamical stability of a many-body Kapitza pendulum
journal, September 2015


Interaction-stabilized steady states in the driven O ( N ) model
journal, May 2016


Phase Structure of Driven Quantum Systems
journal, June 2016


Floquet Time Crystals
journal, August 2016


Absolute stability and spatiotemporal long-range order in Floquet systems
journal, August 2016


Discrete Time Crystals: Rigidity, Criticality, and Realizations
journal, January 2017


Defining time crystals via representation theory
journal, September 2017


Fate of a discrete time crystal in an open system
journal, May 2017


Boundary Time Crystals
journal, July 2018


Time crystals in periodically driven systems
journal, September 2018

  • Yao, Norman Y.; Nayak, Chetan
  • Physics Today, Vol. 71, Issue 9
  • DOI: 10.1063/PT.3.4020

Observation of a discrete time crystal
journal, March 2017

  • Zhang, J.; Hess, P. W.; Kyprianidis, A.
  • Nature, Vol. 543, Issue 7644
  • DOI: 10.1038/nature21413

Observation of discrete time-crystalline order in a disordered dipolar many-body system
journal, March 2017

  • Choi, Soonwon; Choi, Joonhee; Landig, Renate
  • Nature, Vol. 543, Issue 7644
  • DOI: 10.1038/nature21426

Observation of Discrete-Time-Crystal Signatures in an Ordered Dipolar Many-Body System
journal, May 2018


P 31 NMR study of discrete time-crystalline signatures in an ordered crystal of ammonium dihydrogen phosphate
journal, May 2018


Thermal Agitation of Electric Charge in Conductors
journal, July 1928


Reliable computation with cellular automata
journal, February 1986


Stability of temporally periodic states of classical many-body systems
journal, February 1990


Statistical mechanics of cellular automata
journal, July 1983


Subharmonic resonance in the non-linear Mathieu equation
journal, January 2002


Jacobi zeta function and action-angle coordinates for the pendulum
journal, March 2013


Current‐Voltage Characteristics of Josephson Junctions
journal, April 1968


Effect of ac Impedance on dc Voltage‐Current Characteristics of Superconductor Weak‐Link Junctions
journal, June 1968

  • McCumber, D. E.
  • Journal of Applied Physics, Vol. 39, Issue 7
  • DOI: 10.1063/1.1656743

Reaction-rate theory: fifty years after Kramers
journal, April 1990

  • Hänggi, Peter; Talkner, Peter; Borkovec, Michal
  • Reviews of Modern Physics, Vol. 62, Issue 2
  • DOI: 10.1103/RevModPhys.62.251

Thermal activation in extremely underdamped Josephson-junction circuits
journal, August 1983


Fluctuational phase-flip transitions in parametrically driven oscillators
journal, May 1998


A Nuclear Spin System at Negative Temperature
journal, January 1951


Negative Absolute Temperature for Motional Degrees of Freedom
journal, January 2013


Маятник с вибрирующим подвесом
journal, January 1951


Nonlinear mobility of the generalized Frenkel-Kontorova model
journal, March 1997


Hysteresis in the Underdamped Driven Frenkel-Kontorova Model
journal, November 1997


Resonant steps and spatiotemporal dynamics in the damped dc-driven Frenkel-Kontorova chain
journal, September 1998


Dynamics of droplet fluctuations in pure and random Ising systems
journal, May 1987


Colloquium : Modeling friction: From nanoscale to mesoscale
journal, April 2013

  • Vanossi, Andrea; Manini, Nicola; Urbakh, Michael
  • Reviews of Modern Physics, Vol. 85, Issue 2
  • DOI: 10.1103/RevModPhys.85.529

Tuning friction atom-by-atom in an ion-crystal simulator
journal, June 2015


Microwave Characterization of Josephson Junction Arrays: Implementing a Low Loss Superinductance
journal, September 2012


Temporally periodic phases and kinetic roughening
journal, June 1993


Stability and pre-thermalization in chains of classical kicked rotors
journal, October 2018

  • Rajak, Atanu; Citro, Roberta; Dalla Torre, Emanuele G.
  • Journal of Physics A: Mathematical and Theoretical, Vol. 51, Issue 46
  • DOI: 10.1088/1751-8121/aae294

Floquet prethermalization in periodically driven classical spin systems
journal, September 2018


Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems
journal, January 2017


Statistical Dynamics of Classical Systems
journal, July 1973


Topological Defects in Anisotropic Driven Open Systems
journal, August 2018


Kuramoto dynamics in Hamiltonian systems
journal, September 2014


The Kuramoto model: A simple paradigm for synchronization phenomena
journal, April 2005

  • Acebrón, Juan A.; Bonilla, L. L.; Pérez Vicente, Conrad J.
  • Reviews of Modern Physics, Vol. 77, Issue 1
  • DOI: 10.1103/RevModPhys.77.137