Higher-order and fractional discrete time crystals in clean long-range interacting systems
Discrete time crystals are periodically driven systems characterized by a response with periodicity n T , 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...
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| Published in | Nature communications Vol. 12; no. 1; pp. 2341 - 7 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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London
Nature Publishing Group UK
20.04.2021
Nature Publishing Group Nature Portfolio |
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| Abstract | Discrete time crystals are periodically driven systems characterized by a response with periodicity
n
T
, 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’ discrete time crystals with integer and, surprisingly, even fractional
n
> 2. We characterize these (arguably prethermal) non-equilibrium phases of matter thoroughly using a combination of exact diagonalization, semiclassical methods, and spin-wave approximations, which enable us to establish their stability in the presence of competing long- and short-range interactions. Remarkably, these phases emerge in a model with continous driving and time-independent interactions, convenient for experimental implementations with ultracold atoms or trapped ions.
Discrete time crystals are typically characterized by a period doubled response with respect to an external drive. Here, the authors predict the emergence of rich dynamical phases with higher-order and fractional periods in clean spin-1/2 chains with long-range interactions. |
|---|---|
| AbstractList | 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’ discrete time crystals with integer and, surprisingly, even fractional n > 2. We characterize these (arguably prethermal) non-equilibrium phases of matter thoroughly using a combination of exact diagonalization, semiclassical methods, and spin-wave approximations, which enable us to establish their stability in the presence of competing long- and short-range interactions. Remarkably, these phases emerge in a model with continous driving and time-independent interactions, convenient for experimental implementations with ultracold atoms or trapped ions.Discrete time crystals are typically characterized by a period doubled response with respect to an external drive. Here, the authors predict the emergence of rich dynamical phases with higher-order and fractional periods in clean spin-1/2 chains with long-range interactions. 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' discrete time crystals with integer and, surprisingly, even fractional n > 2. We characterize these (arguably prethermal) non-equilibrium phases of matter thoroughly using a combination of exact diagonalization, semiclassical methods, and spin-wave approximations, which enable us to establish their stability in the presence of competing long- and short-range interactions. Remarkably, these phases emerge in a model with continous driving and time-independent interactions, convenient for experimental implementations with ultracold atoms or trapped ions. Discrete time crystals are periodically driven systems characterized by a response with periodicity n T , 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’ discrete time crystals with integer and, surprisingly, even fractional n > 2. We characterize these (arguably prethermal) non-equilibrium phases of matter thoroughly using a combination of exact diagonalization, semiclassical methods, and spin-wave approximations, which enable us to establish their stability in the presence of competing long- and short-range interactions. Remarkably, these phases emerge in a model with continous driving and time-independent interactions, convenient for experimental implementations with ultracold atoms or trapped ions. Discrete time crystals are typically characterized by a period doubled response with respect to an external drive. Here, the authors predict the emergence of rich dynamical phases with higher-order and fractional periods in clean spin-1/2 chains with long-range interactions. Discrete time crystals are typically characterized by a period doubled response with respect to an external drive. Here, the authors predict the emergence of rich dynamical phases with higher-order and fractional periods in clean spin-1/2 chains with long-range interactions. 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' discrete time crystals with integer and, surprisingly, even fractional n > 2. We characterize these (arguably prethermal) non-equilibrium phases of matter thoroughly using a combination of exact diagonalization, semiclassical methods, and spin-wave approximations, which enable us to establish their stability in the presence of competing long- and short-range interactions. Remarkably, these phases emerge in a model with continous driving and time-independent interactions, convenient for experimental implementations with ultracold atoms or trapped ions.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' discrete time crystals with integer and, surprisingly, even fractional n > 2. We characterize these (arguably prethermal) non-equilibrium phases of matter thoroughly using a combination of exact diagonalization, semiclassical methods, and spin-wave approximations, which enable us to establish their stability in the presence of competing long- and short-range interactions. Remarkably, these phases emerge in a model with continous driving and time-independent interactions, convenient for experimental implementations with ultracold atoms or trapped ions. Discrete time crystals are periodically driven systems characterized by a response with periodicity n T , 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’ discrete time crystals with integer and, surprisingly, even fractional n > 2. We characterize these (arguably prethermal) non-equilibrium phases of matter thoroughly using a combination of exact diagonalization, semiclassical methods, and spin-wave approximations, which enable us to establish their stability in the presence of competing long- and short-range interactions. Remarkably, these phases emerge in a model with continous driving and time-independent interactions, convenient for experimental implementations with ultracold atoms or trapped ions. |
| ArticleNumber | 2341 |
| Author | Knolle, Johannes Nunnenkamp, Andreas Pizzi, Andrea |
| Author_xml | – sequence: 1 givenname: Andrea orcidid: 0000-0002-6714-7360 surname: Pizzi fullname: Pizzi, Andrea organization: Cavendish Laboratory, University of Cambridge – sequence: 2 givenname: Johannes orcidid: 0000-0002-0956-2419 surname: Knolle fullname: Knolle, Johannes email: j.knolle@tum.de organization: Department of Physics, Technische Universität München, Munich Center for Quantum Science and Technology (MCQST), Blackett Laboratory, Imperial College London – sequence: 3 givenname: Andreas orcidid: 0000-0003-2390-7636 surname: Nunnenkamp fullname: Nunnenkamp, Andreas organization: School of Physics and Astronomy and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/33879787$$D View this record in MEDLINE/PubMed |
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| Snippet | Discrete time crystals are periodically driven systems characterized by a response with periodicity
n
T
, with
T
the period of the drive and
n
> 1. Typically,... 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... Discrete time crystals are typically characterized by a period doubled response with respect to an external drive. Here, the authors predict the emergence of... |
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| SubjectTerms | 639/766/119/2795 639/766/483/1139 Approximation Crystals Discrete time systems Equilibrium Hilbert space Humanities and Social Sciences Integers Laboratories Magnetic fields multidisciplinary Periodicity Phases Physics Science Science (multidisciplinary) Symmetry |
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| Title | Higher-order and fractional discrete time crystals in clean long-range interacting systems |
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