  In the hole-doped cuprates, the pseudogap refers to a suppression of the
density of states at low energies, in the absence of superconducting long-range
order. Numerous calculations of the Hubbard model show a pseudogap in the
single-particle spectra, with striking similarities to photoemission and
tunneling experiments on cuprates. However, no clear mechanism has been
established. Here, we solve the Hubbard model on $2\times2$ clusters by exact
diagonalization, with integration over twisted boundary conditions. A pseudogap
is found in the single-particle density of states with the following
characteristics: a decreasing energy scale and onset temperature for increased
hole-doping, closure at a critical hole doping near 15\%, absence upon
electron-doping, particle-hole asymmetry indicated by the location of the gap
center, and persistence in the strong-coupling limit of $U/t \to \infty$.
Studying the many-body excitation spectrum reveals that the pseudogap in
single-particle spectra is due to orthogonality between bare electrons and the
lowest energy excitations for $U/t \gtrsim 8$.
