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 »
- Authors:
-
[1];
- Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Microsoft Research, Santa Barbara, CA (United States)
- Univ. of California, Santa Barabara, CA (United States)
- Princeton Univ., NJ (United States)
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Laboratory (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 Volume: 16; Journal ID: ISSN 1745-2473
- Publisher:
- Nature Publishing Group (NPG)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 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. https://doi.org/10.1038/s41567-019-0782-3
Yao, Norman Y., Nayak, Chetan, Balents, Leon, and Zaletel, Michael P. Mon .
"Classical discrete time crystals". United States. https://doi.org/10.1038/s41567-019-0782-3. https://www.osti.gov/servlets/purl/1603622.
@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 = 16,
place = {United States},
year = {Mon Feb 10 00:00:00 EST 2020},
month = {Mon Feb 10 00:00:00 EST 2020}
}
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