Difference between the one-electron small gap and the wide optical gap in 1-, 2-, and 3-dimensional insulating states coming from the strong Coulomb repulsion

We calculate one-electron density of states (DOS) and light absorption spec tra for 1-, 2-, and 3-dimensional half-filled Hubbard systems by means of a quantum Monte-Carlo simulation. We will show that the DOS has only a small gap while the light absorption spectrum has a relatively wide gap. Though the one-electron gap in the DOS slightly increases with dimension, it is al ways smaller than the two-electron gap in the light absorption spectrum. Ou r result indicates that the gap given by the photoemission (or the inverse photoemission) spectrum is smaller than the optical gap. (C) 1999 Elsevier Science BN. All rights reserved.