Pseudogap is a ubiquitous phenomenon in strongly correlated systems such as high-$T_{rm c}$ superconductors, ultracold atoms and nuclear physics. While pairing fluctuations inducing the pseudogap are known to be enhanced in low-dimensional systems, such effects have not been explored well in one of the most fundamental 1D models, that is, Gaudin-Yang model. In this work, we show that the pseudogap effect can be visible in the single-particle excitation in this system using a diagrammatic approach. Fermionic single-particle spectra exhibit a unique crossover from the double-particle dispersion to pseudogap state with increasing the attractive interaction and the number density at finite temperature. Surprisingly, our results of thermodynamic quantities in unpolarized and polarized gases show an excellent agreement with the recent quantum Monte Carlo and complex Langevin results, even in the region where the pseudogap appears.
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