Finite-temperature exact diagonalization cluster dynamical mean-field study of the two-dimensional Hubbard model: Pseudogap, non-Fermi-liquid behavior, and particle-hole asymmetry

Abstract

The effect of doping in the two-dimensional Hubbard model is studied within finite-temperature exact diagonalization combined with cluster dynamical mean-field theory. By employing a mixed basis involving cluster sites and bath molecular orbitals for the projection of the lattice Green's function onto $2\ifmmode\times\else\texttimes\fi{}2$ clusters, a considerably more accurate description of the low-frequency properties of the self-energy is achieved than in a pure site picture. To evaluate the phase diagram, the transition from Fermi-liquid to non-Fermi-liquid behavior for decreasing hole doping is studied as a function of Coulomb energy, next-nearest-neighbor hopping, and temperature. The self-energy component ${\ensuremath{\Sigma}}_{X}$ associated with $X=(\ensuremath{\pi},0)$ is shown to develop a collective mode above ${E}_{F}$, whose energy and strength exhibits a distinct dispersion with doping. This low-energy excitation gives rise to non-Fermi-liquid behavior as the hole doping decreases below a critical value ${\ensuremath{\delta}}_{c}$, and to an increasing particle-hole asymmetry, in agreement with recent photoemission data. This behavior is consistent with the removal of spectral weight from electron states above ${E}_{F}$ and the opening of a pseudogap, which increases with decreasing doping. The phase diagram reveals that ${\ensuremath{\delta}}_{c}\ensuremath{\approx}0.15\dots{}0.20$ for various system parameters. For electron doping, the collective mode of ${\ensuremath{\Sigma}}_{X}(\ensuremath{\omega})$ and the concomitant pseudogap are located below the Fermi energy, which is consistent with the removal of spectral weight from the hole states just below ${E}_{F}$. The critical doping, which marks the onset of non-Fermi-liquid behavior, is systematically smaller than for hole doping.