Anomalies in the pseudogap phase of the cuprates: Competing ground states and the role of umklapp scattering

Over the past two decades, advances in computational algorithms haverevealed a curious property of the two-dimensional Hubbard model (andrelated theories) with hole doping: the presence of close-in-energycompeting ground states that display very different physical properties.On the one hand, there is a complicated state exhibiting intertwinedspin, charge, and pair density wave orders. We call this 'type A'. Onthe other hand, there is a uniform d-wave superconducting state that wedenote as 'type B'. We advocate, with the support of both microscopictheoretical calculations and experimental data, dividing thehigh-temperature cuprate superconductors into two correspondingfamilies, whose properties reflect either the type A or type B groundstates at low temperatures. We review the anomalous properties of thepseudogap phase that led us to this picture, and present a modernperspective on the role that umklapp scattering plays in these phenomenain the type B materials. This reflects a consistent framework that hasemerged over the last decade, in which Mott correlations at weakcoupling drive the formation of the pseudogap. We discuss thisdevelopment, recent theory and experiments, and open issues.