We calculate the fermionic spectral function Ak(ω) in the spiral spin density wave (SDW) state of the Hubbard model on a quasi-2D triangular lattice at small but finite temperature T. The spiral SDW order Δ(T) develops below T=TN and has momentum K=(4π/3,0). We pay special attention to fermions with momenta k, for which k and k+K are close to Fermi surface in the absence of SDW. At the mean-field level, Ak(ω) for such fermions has peaks at ω=±Δ(T) at T<TN and displays a conventional Fermi liquid behavior at T>TN. We show that this behavior changes qualitatively beyond mean field due to singular self-energy contributions from thermal fluctuations in a quasi-2D system. We use a nonperturbative eikonal approach and sum up infinite series of thermal self-energy terms. We show that Ak(ω) shows peak/dip/hump features at T<TN, with the peak position at Δ(T) and hump position at Δ(T=0). Above TN, the hump survives up to T=Tp>TN, and in between TN and Tp the spectral function displays the pseudogap behavior. We show that the difference between Tp and TN is controlled by the ratio of in-plane and out-of-plane static spin susceptibilities, which determines the combinatoric factors in the diagrammatic series for the self-energy. For certain values of this ratio, Tp=TN, i.e., the pseudogap region collapses. In this last case, thermal fluctuations are logarithmically singular, yet they do not give rise to pseudogap behavior. Our computational method can be used to study pseudogap physics due to thermal fluctuations in other systems.
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We thank Liang Fu, Antoine Georges, Emanuel Gull, Evgeny Kozik, James P.F. LeBlanc, Jörg Schmalian, Fedor Simkovic, and Zhengkang Zhang for helpful discussions. The work was supported by the NSF DMR-1523036. M.Y. also acknowledges support from Louise Dosdall Fellowship from the University of Minnesota.