Insulator, conductor, and commensurability: a topological approach.
I discuss a topological relation of the conduction property of a many-particle system on a periodic lattice at zero temperature to the energy spectrum. When the particle number per unit cell is an irreducible fraction p/q, an insulator must have q low-lying states of energy O(1/L) in one dimension and of energy O(1) in two dimensions, where L is the linear system size.
Oshikawa
Masaki
M
Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan.