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\u2013prey 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. Finally, 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. The phenomenon of many-body localization gives rise to entirely new phases of quantum matter when it is driven away from equilibrium. A numerical study now shows that one of these phases\u2014the discrete time crystal\u2014can also occur in a classical spin chain.<\/p>\n","protected":false},"excerpt":{"rendered":"
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 […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[243138],"msr-publication-type":[193715],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-field-of-study":[251155,251131,248242,251152,251146,251143,249739,249337,250069,251149],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-721537","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-quantum","msr-locale-en_us","msr-field-of-study-classical-mechanics","msr-field-of-study-discrete-time-and-continuous-time","msr-field-of-study-dynamical-systems-theory","msr-field-of-study-ergodicity","msr-field-of-study-faraday-wave","msr-field-of-study-hamiltonian-mechanics","msr-field-of-study-phase-transition","msr-field-of-study-physics","msr-field-of-study-quantum","msr-field-of-study-stochastic-cellular-automaton"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"2020-3-31","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"","msr_chapter":"","msr_isbn":"","msr_journal":"2020 Nature Physics","msr_volume":"16","msr_number":"","msr_editors":"","msr_series":"","msr_issue":"4","msr_organization":"","msr_how_published":"","msr_notes":"","msr_highlight_text":"","msr_release_tracker_id":"","msr_original_fields_of_study":"","msr_download_urls":"","msr_external_url":"","msr_secondary_video_url":"","msr_longbiography":"","msr_microsoftintellectualproperty":1,"msr_main_download":"","msr_publicationurl":"","msr_doi":"","msr_publication_uploader":[{"type":"doi","viewUrl":"false","id":"false","title":"10.1038\/S41567-019-0782-3","label_id":"243106","label":0},{"type":"url","viewUrl":"false","id":"false","title":"https:\/\/www.nature.com\/articles\/s41567-019-0782-3.epdf","label_id":"243132","label":0}],"msr_related_uploader":"","msr_attachments":[],"msr-author-ordering":[{"type":"text","value":"Norman Y. 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