A Brief History of Time Crystals

Abstract

The idea of breaking time-translation symmetry has fascinated humanity at least since ancient proposals of the perpetuum mobile. Unlike the breaking of other symmetries, such as spatial translation in a crystal or spin rotation in a magnet, time translation symmetry breaking (TTSB) has been tantalisingly elusive. We review this history up to recent developments which have shown that discrete TTSB does takes place in periodically driven (Floquet) systems in the presence of many-body localization. Such Floquet time-crystals represent a new paradigm in quantum statistical mechanics --- that of an intrinsically out-of-equilibrium many-body phase of matter. We include a compendium of necessary background, before specializing to a detailed discussion of the nature, and diagnostics, of TTSB. We formalize the notion of a time-crystal as a stable, macroscopic, conservative clock --- explaining both the need for a many-body system in the infinite volume limit, and for a lack of net energy absorption or dissipation. We also cover a range of related phenomena, including various types of long-lived prethermal time-crystals, and expose the roles played by symmetries -- exact and (emergent) approximate -- and their breaking. We clarify the distinctions between many-body time-crystals and other ostensibly similar phenomena dating as far back as the works of Faraday and Mathieu. En route, we encounter Wilczek's suggestion that macroscopic systems should exhibit TTSB in their ground states, together with a theorem ruling this out. We also analyze pioneering recent experiments detecting signatures of time crystallinity in a variety of different platforms, and provide a detailed theoretical explanation of the physics in each case. In all existing experiments, the system does not realize a `true' time-crystal phase, and we identify necessary ingredients for improvements in future experiments.

Invited Review article; 70 pages

References in corpus (2)

• Trojan quasiparticles
• Stabilizing a discrete time crystal against dissipation

Cited by in corpus (53)

• Observation of a prethermal discrete time crystal
• Fractal, logarithmic and volume-law entangled non-thermal steady states via spacetime duality
• All-Optical Dissipative Discrete Time Crystals
• A constructive theory of the numerically accessible many-body localized to thermal crossover
• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Engineered dissipation induced entanglement transition in quantum spin chains: from logarithmic growth to area law
• Floquet engineering of topological localization transitions and mobility edges in one-dimensional non-Hermitian quasicrystals
• Long-lived period-doubled edge modes of interacting and disorder-free Floquet spin chains
• Scaling of temporal entanglement in proximity to integrability
• Topological and symmetry-enriched random quantum critical points
• Creating and controlling global Greenberger-Horne-Zeilinger entanglement on quantum processors
• Topological two-dimensional Floquet lattice on a single superconducting qubit
• Driving-induced multiple $\mathcal{P}\mathcal{T}$-symmetry breaking transitions and reentrant localization transitions in non-Hermitian Floquet quasicrystals
• Signatures of discrete time-crystallinity in transport through an open Fermionic chain
• Square-root Floquet topological phases and time crystals
• Genuine Multipartite Correlations in a Boundary Time Crystal
• Observing Floquet topological order by symmetry resolution
• Critical properties of the prethermal Floquet Time Crystal
• Six-dimensional time-space crystalline structures
• Emergence and Dynamical Stability of Charge Time-Crystal in a Current-Carrying Quantum Dot Simulator
• Floquet Prethermal Phase Protected by U(1) Symmetry on a Superconducting Quantum Processor
• Stroboscopic aliasing in long-range interacting quantum systems
• Polynomial filter diagonalization of large Floquet unitary operators
• Critical properties of the Floquet time crystal within the Gaussian approximation
• Protecting Quantum Information in Quantum Dot Spin Chains by Driving Exchange Interactions Periodically
• Random matrix theory for quantum and classical metastability in local Liouvillians
• Simulation of many body localization and time crystals in two dimensions with the neighborhood tensor update
• Topological Defects in Floquet Circuits
• Spacetime magnetic hopfions: from internal excitations and braiding of skyrmions
• Topological and dynamical features of periodically driven spin ladders
• Nonlocal discrete time crystals in periodically driven surface codes
• Criticality and Rigidity of Dissipative Discrete Time Crystals in Solids
• Anomalous Random Multipolar Driven Insulators
• Fisher zeros and persistent temporal oscillations in non-unitary quantum circuits
• Inseparable time-crystal geometries on the Möbius strip
• Route to Extend the Lifetime of a Discrete Time Crystal in a Finite Spin Chain Without Disorder
• Topological $\pi$ modes and beyond
• Comment on "Quantum Time Crystals from Hamiltonians with Long-Range Interactions"
• Non-Hermitian quantum gases: a platform for imaginary time crystals
• How periodic driving stabilises and destabilises Anderson localisation on random trees
• Quantum quench in a driven Ising chain
• Basis for time crystal phenomena in ultra-cold atoms bouncing on an oscillating mirror
• Fragility to quantum fluctuations of classical Hamiltonian period doubling
• Absence of temporal order in states with spatial correlation decay
• Ancilla assisted Discrete Time Crystals in Non-interacting Spin Systems
• Quantum Correlations in Space-Time: Foundations and Applications
• Determination of magnon mass of neodymium magnet by temperature dependence of spontaneous magnetization
• $2+1$ dimensional Floquet systems and lattice fermions: Exact bulk spectral equivalence
• Strong and almost strong modes of Floquet spin chains in Krylov subspaces
• Long-time properties of generic Floquet systems are approximately periodic with the driving period
• Reply to Comment on "Discrete Time Crystals: Rigidity Criticality and Realizations"
• Discrete time crystals in Bose-Einstein Condensates and symmetry-breaking edge in a simple two-mode theory
• A comment on "Discrete time crystals: rigidity, criticality, and realizations"