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We calculate the fermionic spectral function $A_k (\omega)$ in the spiralspin-density-wave (SDW) state of the Hubbard model on a quasi-2D triangularlattice at small but finite temperature $T$. The spiral SDW order $\Delta (T)$develops below $T = T_N$ and has momentum ${ \bf K} = (4\pi/3,0)$. We payspecial attention to fermions with momenta ${\bf k}$, for which ${\bf k}$ and${\bf k} + {\bf K}$ are close to Fermi surface in the absence of SDW. At themean field level, $A_k (\omega)$ for such fermions has peaks at $\omega = \pm\Delta (T)$ at $T < T_N$ and displays a conventional Fermi liquid behavior at$T > T_N$. We show that this behavior changes qualitatively beyond mean-fielddue to singular self-energy contributions from thermal fluctuations in aquasi-2D system. We use a non-perturbative eikonal approach and sum up infiniteseries of thermal self-energy terms. We show that $A_k (\omega)$ showspeak/dip/hump features at $T < T_N$, with the peak position at $\Delta (T)$ andhump position at $\Delta (T=0)$. Above $T_N$, the hump survives up to $T = T_p> T_N$, and in between $T_N$ and $T_p$ the spectral function displays thepseudogap behavior. We show that the difference between $T_p$ and $T_N$ iscontrolled by the ratio of in-plane and out-of-plane static spinsusceptibilities, which determines the combinatoric factors in the diagrammaticseries for the self-energy. For certain values of this ratio, $T_p = T_N$,i.e., the pseudogap region collapses. In this last case, thermal fluctuationsare logarithmically singular, yet they do not give rise to pseudogap behavior.Our computational method can be used to study pseudogap physics due to thermalfluctuations in other systems.

The Hubbard model on a triangular lattice -- pseudogap due to spin-density-wave fluctuations