Discrete Lorentz symmetry and discrete spacetime translational symmetry in two- and three-dimensional crystals

Abstract

As is well known, crystals have discrete space translational symmetry. It was recently noticed that one-dimensional crystals possibly have discrete Poincaré symmetry, which contains discrete Lorentz and discrete time translational symmetry as well. In this paper, we classify the discrete Poincaré groups on two- and three-dimensional Bravais lattices. They are the candidate symmetry groups of two- or three-dimensional crystals, respectively. The group is determined by an integer generator $g$, and it reduces to the space group of crystals at $g=2$.

arXiv comment8 pages, 2 figures

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Cited by in corpus (2)

• Poincaré crystal on the one-dimensional lattice
• The mixing-spacetime symmetry in the Floquet-Bloch band theory