Space-time crystal and space-time group

Abstract

Crystal structures and the Bloch theorem play a fundamental role in condensed matter physics. We extend the static crystal to the dynamic "space-time" crystal characterized by the general intertwined space-time periodicities in $D+1$ dimensions, which include both the static crystal and the Floquet crystal as special cases. A new group structure dubbed "space-time" group is constructed to describe the discrete symmetries of space-time crystal. Compared to space and magnetic groups, space-time group is augmented by "time-screw" rotations and "time-glide" reflections involving fractional translations along the time direction. A complete classification of the 13 space-time groups in 1+1D is performed. The Kramers-type degeneracy can arise from the glide time-reversal symmetry without the half-integer spinor structure, which constrains the winding number patterns of spectral dispersions. In 2+1D, non-symmorphic space-time symmetries enforce spectral degeneracies, leading to protected Floquet semi-metal states. Our work provides a general framework for further studying topological properties of the $D+1$ dimensional space-time crystal.

arXiv comment4+5 pages, 7 figures

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Cited by in corpus (43)

• Topology and Broken Symmetry in Floquet Systems
• Floquet second-order topological insulators from nonsymmorphic space-time symmetries
• Dynamical synchronization transition in interacting electron systems
• Condensed Matter Physics in Time Crystals
• Topological Time Crystals
• Topological pumping in a Floquet-Bloch band
• Topological space-time crystal
• Conversion between electron spin and microscopic atomic rotation
• Tunable space-time crystal in room-temperature magnetodielectrics
• Floquet engineering of individual band gaps in an optical lattice using a two-tone drive
• Floquet-Bloch Oscillations and Intraband Zener Tunneling in an Oblique Spacetime Crystal
• Floquet superradiance lattices in thermal atoms
• Floquet quadrupole photonic crystals protected by space-time symmetry
• Space-time crystalline order of a high-critical-temperature superconductor with intrinsic Josephson junctions
• Topological Quantum Walk with Discrete Time-Glide Symmetry
• Floquet topological insulators: from band structure engineering to novel non-equilibrium quantum phenomena
• Interacting topological mirror excitonic insulator in one dimension
• Prethermal time-crystalline spin ice and monopole confinement in a driven magnet
• Electron Scattering at a Potential Temporal Step Discontinuity
• Semiclassical dynamics of electrons in space-time crystal: Magnetization, polarization, and current response
• Dynamical Fragile Topology in Floquet Crystals
• Topological charge pumping in spin-dependent superlattices with glide symmetry
• Localization of matter waves in lattice systems with moving disorder
• Space-time symmetry breaking in nonequilibrium frustrated magnetism
• Non-Bloch Theory for Spatiotemporal Photonic Crystals Assisted by Continuum Effective Medium
• Distinct Floquet topological classifications from color-decorated frequency lattices with space-time symmetries
• A Solvable Model for Discrete Time Crystal Enforced by Nonsymmorphic Dynamical Symmetry
• Space-time symmetry and nonreciprocal parametric resonance in mechanical systems
• The Future of the Correlated Electron Problem
• Classification of same-gate quantum circuits and their space-time symmetries with application to the level-spacing distribution
• Projective Spacetime Symmetry of Spacetime Crystals
• Dynamical characterization of $Z_2$ Floquet topological phases via quantum quenches
• The Symmetry Principle in Condensed Matter Physics (I)
• Floquet Möbius topological insulators
• Critical spacetime crystals in continuous dimensions
• Spacetime symmetry indicators for two-dimensional Floquet topological insulators
• Dynamical Symmetry Indicators for Floquet Crystals
• Access to Klein Tunneling via Space-Time Modulation
• Engineering micromotion in Floquet prethermalization via space-time symmetries
• The mixing-spacetime symmetry in the Floquet-Bloch band theory
• Intrinsic space-time crystalline order in a hybrid Josephson junction
• Topological Classification of Gapped/Gap-preserving Rational Space-Time Crystal Systems
• Atomic Regional Superfluids in two-dimensional Moiré Time Crystals