  Combined with Laughlin's argument on the quantized Hall conductivity,
Lieb-Schultz-Mattis argument is extended to quantum many-particle systems
(including quantum spin systems) with a conserved particle number, on a
periodic lattice in arbitrary dimensions. Regardless of dimensionality,
interaction strength and particle statistics (bose/fermi), a finite excitation
gap is possible only when the particle number per unit cell of the groundstate
is an integer.
