Incipient antiferromagnetism and low-energy excitations in the half-filled two-dimensional Hubbard model.

We present single-particle and thermodynamic properties of the half-filled single-band Hubbard model in 2D calculated in the self-consistent fluctuation exchange approximation. The low-energy excitations at moderate temperatures and small U are quasiparticles with a short lifetime. As the temperature is lowered, coupling to evolving spin fluctuations leads to the extinction of these quasiparticles, signaled by a weak pseudogap in the density of states and by a positive slope in Re Σ(kF , ε) and a local maximum in |Im Σ(kF , ε)| at ε = 0. We explain these results using a simple spin-fluctuation model. 71.27.+a, 75.10.Lp, 75.30.Kz Typeset using REVTEX 1 The 2D single-band Hubbard model plays a central role in efforts to understand the behavior of electrons near the Fermi surface in the cuprate superconductors and their parent compounds [1]. The model is characterized by a nearest-neighbor hopping energy, t, and an on-site Coulomb energy, U . For a half-filled band, the T = 0 state is believed to be an antiferromagnetic insulator for all U > 0 [2,3]. For T > 0, the Mermin-Wagner theorem precludes the existence of long-range AFM order in 2D, but with strong coupling (U > ∼ 8t) the low-temperature electronic state is almost certainly a Mott insulator. With U = 4t and 0.10t < ∼ T < ∼ 0.25t, conflicting results have been obtained from quantum Monte Carlo (QMC) calculations of the one-electron spectral weight function, A(k, ε), depending on lattice size and especially on the method used to extract A(k, ε) from the Green’s function G(k, τ) produced directly by QMC. Spectral functions on the Fermi surface (FS) produced by the maximum entropy technique show a single peak whenever the lattice is larger than the AFM correlation length, but develop a pseudogap on smaller lattices [4]. In contrast, recent calculations using the method of singular value decomposition yield a pseudogap in both the spectral function on the FS and in the total density of states, N(ε) = N ∑ k A(k, ε), even for lattices larger than the correlation length [5]. We report calculations of A(k, ε) and N(ε) at half-filling and moderate U (< 4.8t) using the fluctuation exchange approximation (FEA), a self-consistent conserving approximation that has been applied to the 2D Hubbard model in a number of recent papers [6–8]. In particular, the FEA has been used to argue for a d-wave superconducting transition in the high-Tc cuprates [8]; the need to evaluate these claims adds to the importance of knowing what the FEA predicts (rightly or wrongly) for the normal state at half-filling. Compared to QMC, the FEA has the disadvantage that it is inherently an approximation, though imaginary-time Green’s functions from the FEA and QMC agree surprisingly well at halffilling and moderate U [6]. For studying the spectral function and DOS, the FEA has several important advantages over QMC: (1) There is no inherently statistical error in the FEA results, which removes most of the uncertainty in extracting A(k, ε) from G(k, τ). (2) FEA calculations are possible for large enough lattices (typically 128× 128) to ensure that