Strong-coupling mechanism of the pseudogap in small Hubbard clusters

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 $U/t \gtrsim 8$.