Archive of posts with tag “lattice”

• Nov 9, 2023

  Rotational symmetry of plane lattices as a simple example of algebraic number theory

  For a plane lattice, there is only a finite number of different rotational symmetries that are compatible with the discrete translational symmetry. For example, the 5-fold rotational symmetry is not one of them. Why is that? It turns out that whether an $m$-fold symmetry is compatible with translational symmetry is the same as whether $\varphi(m)\le2$.

  • Categories: math
  • Tags: complex, condensed matter physics, algebraic number theory, lattice, mathematical physics