Title: Ground state degeneracy in quantum spin systems protected by crystal symmetries,
Abstract: We develop a no-go theorem for two-dimensional bosonic systems with crystal
symmetries: if there is a half-integer spin at a rotation center, where the
point-group symmetry is $\mathbb D_{2,4,6}$, such a system must have a
ground-state degeneracy protected by the crystal symmetry. Such a degeneracy
indicates either a broken-symmetry state or a unconventional state of matter.
Comparing to the Lieb-Schultz-Mattis Theorem, our result counts the spin at
each rotation center, instead of the total spin per unit cell, and therefore
also applies to certain systems with an even number of half-integer spins per
unit cell.