Effect of next-nearest neighbor hopping on the single-particle excitations

Abstract

In the half-filled one-orbital Hubbard model on a square lattice, we study the effect of next-nearest neighbor hopping on the single-particle spectral function at finite temperature using an exact-diagonalization + Monte-Carlo based approach to the simulation process. We find that the pseudogap-like dip, existing in the density of states in between the Néel temperature $T_N$ and a relatively higher temperature $T^{\ast }$, is accompanied with a significant asymmetry in the hole- and particle-excitation energy along the high-symmetry directions as well as along the normal-state Fermi surface. On moving from ($\pi /2,\pi /2$) toward $(\pi ,0)$ along the normal state Fermi surface, the hole-excitation energy increases, a behavior remarkably similar to what is observed in the $d$-wave state and pseudogap phase of high-$T_c$ cuprates, whereas the particle-excitation energy decreases. The quasiparticle peak height is the largest near ($\pi /2,\pi /2$) whereas it is the smallest near $(\pi ,0)$. These spectral features survive beyond $T_N$. The temperature window $T_N\lesssim T\lesssim T^{\ast }$ shrinks with an increase in the next-nearest neighbor hopping, which indicates that the next-nearest neighbor hopping may not be supportive to the pseudogap-like features.

7 pages, 7 figures