What is the simplest model that captures the basic experimental facts of the physics of underdoped cuprates?

The discovery of cuprates has been underlined by two salient phenomena, their high-temperature superconductivity (SC) and the occurrence of the “pseudogap” (PG) in the underdoped part of the hole-doped phase diagram, with a large set of associated fascinating physical properties. A large debate has been opened more than ten years ago about the actual significance of the pseudogap: signature of preformed pairs or independent order in competition with SC. This debate was apparently on the verge to be cleared in favour of the competing order scenario. Indeed a series of recent experiments done with distinct experimental techniques report charge ordered (CDW) or symmetry broken states in the underdoped cuprates. Some speculations based on theoretical calculations suggest that those observations reveal a totally different origin than expected initially for the superconductivity in the cuprates. These new speculations justify recalling some of the experimental results that have been established on the early days of High Temperature SC and which have been quite often “forgotten”, or “overlooked” by newcomers in the field who tend to consider that the pseudogap onset temperature T ⁎ is an ill-defined temperature. I shall recall here that there is no doubt whatsoever from the early days that the onset of the pseudogap state is much higher in temperature than all the recently detected charge-order phenomena in comparable samples, which apparently compete with SC. (Indeed, the onsets of these new states are detected at temperatures at which a 50% decrease of the spin susceptibility has already occurred.) I shall also recall that some of the early mean field theories have initiated the idea that both SC and the PG could be generated within a simple doped Hubbard model, or its simplified t – J model version. Recent calculations extending those to Dynamical Mean Field Theories (DMFT), with more or less sophisticated versions give theoretical determinations of physical quantities which begin to resemble quite nicely most of the experimental observations done below T ⁎ . Direct comparisons are still not secured as they do rely on the approximations done in the DMFT calculations. The basic Hubbard model does not generate the CDW phases, presumably due to symmetry-breaking perturbations present in the actual materials. Though we had underlined in the past that the disorder of the chemical dopants is one of the dominant perturbations, the recent experiments on chain-ordered YBCO suggest that the ordering of the dopants can indeed be influential as well in stabilizing commensurate CDW states. Therefore, the variety of broken symmetry states detected recently at lower temperatures than the pseudogap T ⁎ certainly requires more complicated modelling and are not necessarily generic. They most certainly correspond to specific ground states of the pseudogap electronic matter which exhibit interesting correlated orders.