Thermal evolution of the 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 pseudogap-like features in the form of two-peak structures associated with the momentum-resolved spectral function. These features exist within the temperature window ${T}_N\ensuremath{\lesssim}T\ensuremath{\lesssim}{T}^*$, where ${T}_N$ is the N\'eel temperature and ${T}^*$ is the temperature below which there exists a well-formed dip in the density of state. Inside the window ${T}_N\ensuremath{\lesssim}T\ensuremath{\lesssim}{T}^*$, the peak-to-peak separation in the two-peak structure of the momentum-resolved spectral function grows on moving away from the point ($\ensuremath{\pi}/2,\ensuremath{\pi}/2$) along the normal state Fermi surface toward $(\ensuremath{\pi},0)$, a behavior with remarkable similarities to what is observed in the $d$-wave state and pseudogap phase of high-${T}_c$ cuprates. We unveil these features by using a parallelized cluster-based Monte Carlo method for simulating the magnetic order parameter fields on a superlattice. The method enables us to access the momentum-resolved single-particle spectral function corresponding to a lattice size of $\ensuremath{\approx}240 \ifmmode\times\else\texttimes\fi{}$ 240 with an almost negligible finite-size effect.