Thermal evolution of single-particle spectral function in the half-filled Hubbard model and pseudogap

In the half-filled one-orbital Hubbard model on a square lattice, we find pseduogap features in the form of two-peak structures associated with the momentum-resolved spectral function, which exists within the temperature window $T_N\lesssim T\lesssim T^{\ast }$. $T^{\ast }$ is the temperature below which there exists a well-formed dip in the density of state. Inside the window $T_N\lesssim T\lesssim T^{\ast }$, the peak-to-peak separation in the two-peak structure of the momentum-resolved spectral function rises on moving away from the point ($\pi \mathrm{/}2,\pi \mathrm{/}2$) along the normal state Fermi surface towards $(\pi ,0)$, a behavior remarkably similar to what is observed in the pseudogap phase. We unveil these features by using a parallelized cluster-based Monte-Carlo method for simulating the magnetic order parameter fields on a superlattice, which enables us to access the momentum-resolved single-particle spectral function corresponding to a lattice size of $\sim$ 240 $\times$ 240 with almost negligible finite-size effects.