Title: Symmetry-enforced quantum spin Hall insulators in $π$-flux models,
Abstract: We prove a Lieb-Schultz-Mattis theorem for the quantum spin Hall effect
(QSHE) in two-dimensional $\pi$-flux models. In the presence of time reversal,
$U(1)$ charge conservation and magnetic translation (with $\pi$-flux per unit
cell) symmetries, if a generic interacting Hamiltonian has a unique gapped
symmetric ground state at half filling (i.e. an odd number of electrons per
unit cell), it can only be a QSH insulator. In other words, a trivial Mott
insulator is forbidden by symmetries at half filling. We further show that such
a symmetry-enforced QSHE can be realized in cold atoms, by shaking an optical
lattice and applying a time-dependent Zeeman field.