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Space-Time Crystal and Space-Time Group.

Shenglong Xu1,2, Congjun Wu1

  • 1Department of Physics, University of California, San Diego, California 92093, USA.

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|March 17, 2018
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Summary
This summary is machine-generated.

Researchers introduce dynamic space-time crystals, extending static crystals with intertwined periodicities. They developed space-time groups to classify these structures, revealing new symmetries and spectral degeneracies in condensed matter physics.

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Area of Science:

  • Condensed matter physics
  • Solid-state physics
  • Quantum mechanics

Background:

  • Static crystals and Bloch theorem are foundational in condensed matter physics.
  • Existing models often consider static or Floquet crystals.
  • Need for a framework to describe more general space-time periodicities.

Purpose of the Study:

  • To extend the concept of static crystals to dynamic space-time crystals.
  • To introduce and define space-time groups for describing discrete symmetries.
  • To classify space-time groups and explore their implications for spectral properties.

Main Methods:

  • Development of a new group structure: the space-time group.
  • Classification of 13 space-time groups in 1+1 dimensions.
  • Analysis of spectral degeneracies arising from space-time symmetries in 2+1 dimensions.

Main Results:

  • Introduction of space-time crystals with general intertwined periodicities.
  • Space-time groups include novel operations like time-screw rotations and time-glide reflections.
  • Kramers-type degeneracy observed from glide time-reversal symmetry.
  • Nonsymmorphic space-time symmetries lead to protected Floquet semimetal states in 2+1D.

Conclusions:

  • Space-time crystals offer a broader framework than static or Floquet crystals.
  • Space-time groups provide a systematic way to describe complex symmetries.
  • These findings open avenues for studying topological properties in higher dimensions.