Projective Spacetime Symmetry of Spacetime Crystals
arXiv:2310.09577 · doi:10.1038/s42005-023-01446-z
Abstract
Wigner's seminal work on the Poincaré group revealed one of the fundamental principles of quantum theory: symmetry groups are projectively represented. The condensed-matter counterparts of the Poincaré group could be the spacetime groups of periodically driven crystals or spacetime crystals featuring spacetime periodicity. In this study, we establish the general theory of projective spacetime symmetry algebras of spacetime crystals, and reveal their intrinsic connections to gauge structures. As important applications, we exhaustively classify (1,1)D projective symmetry algebras and systematically construct spacetime lattice models for them all. Additionally, we present three consequences of projective spacetime symmetry that surpass ordinary theory: the electric Floquet-Bloch theorem, Kramers-like degeneracy of spinless Floquet crystals, and symmetry-enforced crossings in the Hamiltonian spectral flows. Our work provides both theoretical and experimental foundations to explore novel physics protected by projective spacetime symmetry of spacetime crystals.
References in corpus (41)
- Topological Photonics
- Topological Photonics
- Topological Crystalline Insulators
- Artificial gauge potentials for neutral atoms
- Topological quantum chemistry
- Photovoltaic Hall effect in graphene
- Topological Acoustics
- Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
- The (High Quality) Topological Materials In The World
- Transport properties of non-equilibrium systems under the application of light: Photo-induced quantum Hall insulators without Landau levels
- Topolectrical circuit realization of topological corner modes
- Floquet Engineering of Quantum Materials
- Topological Bands for Ultracold Atoms
- Catalogue of Topological Electronic Materials
- Towards ideal topological materials: Comprehensive database searches using symmetry indicators
- Exploring Topological Phases With Quantum Walks
- Topology of crystalline insulators and superconductors
- Floquet Spectrum and Transport Through an Irradiated Graphene Ribbon
- Floquet approach to lattice gauge theories with ultracold atoms in optical lattices
- Periodic Table for Floquet Topological Insulators
- Topological phonon modes and their role in dynamic instability of microtubules
- Photoinduced transition between conventional and topological insulators in two-dimensional electronic systems
- Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects
- Observation of an acoustic octupole topological insulator
- Observation of anomalous π modes in photonic Floquet engineering
- Floquet Topological States in Shaking Optical Lattices
- Clean Floquet Time Crystals: Models and Realizations in Cold Atoms
- 4D spinless topological insulator in a periodic electric circuit
- Floquet topological phases protected by time glide symmetry
- Projectively enriched symmetry and topology in acoustic crystals
- Laser-Driven Multiferroics and Ultrafast Spin Current Generation
- Acoustic Möbius insulators from projective symmetry
- Space-time crystal and space-time group
- Switching spinless and spinful topological phases with projective symmetry
- Brillouin Klein Bottle From Artificial Gauge Fields
- The gauge-field extended method and novel topological phases
- Spinful topological phases in acoustic crystals with projective PT symmetry
- Topological space-time crystal
- Classification of time-reversal-invariant crystals with gauge structures
- Hofstadter Topology with Real Space Invariants and Reentrant Projective Symmetries
- Floquet-Bloch Oscillations and Intraband Zener Tunneling in an Oblique Spacetime Crystal