“…This way, the electronic structure and the pseudogap behavior in the Hubbard model and its low-energy t − J models 22 have been revisited many times and studied by a number of different numerical approaches such as quantum Monte-Carlo (QMC) [23][24][25][26][27] , cluster perturbation theory (CPT) 28,29 , variational cluster approximation (VCA) 30 , dynamical mean-field theory (DMFT) 31 and its cluster (CDMFT) 32,33 and diagram 34,35 extensions, and other techniques designed for dealing with strongly correlated systems [36][37][38][39][40] . A large body of theoretical work is concentrated on the doping evolution of the pseudogap, while its temperature dependance still lacks a systematic investigation.…”