Physical quantities in nearly antiferromagnetic and superconducting states of the two-dimensional Hubbard model and comparison with cuprate superconductors

Abstract

We have calculated within the fluctuation exchange approximation the full momentum and real-frequency dependence of the quasiparticle self-energy, the gap function, and the dynamic spin susceptibility for the two-dimensional Hubbard model near half filling. The spin-density-wave (SDW) instability is reached only asymptotically in the limit of infinite U or zero temperature. Near the SDW instability we find approximately marginal Fermi-liquid behavior, a pseudogap in the density of states, and a singlet ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ pairing instability. Below ${\mathit{T}}_{\mathit{c}}$, gaps open rapidly in the frequency spectra of the gap function, the quasiparticle scattering rate, and the density of states. The spectral density of the dynamic spin susceptibility agrees qualitatively with the neutron-scattering data on ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Sr}}_{\mathit{x}}$ ${\mathrm{CuO}}_4$. The quasiparticle scattering rate and spin-lattice relaxation rate ${\mathit{T}}_1^{\mathrm{-}1}$ decrease rapidly below ${\mathit{T}}_{\mathit{c}}$. The photoemission intensities along the antinode and node of the gap are in good agreement with the angle-resolved photoemission spectroscopy data on Bi 2212. Including next-nearest-neighbor hopping we obtain for sufficiently large coupling (U/t≳7) a broad commensurate neutron-scattering peak like the observed one in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6+\mathit{x}}$.