Mott-Slater transition in undoped cuprates

We study phases of short-range magnetic order by coupling different density-wave modes with a self-consistent vertex correction. By tuning the band structure we are able to transform between different cuprates, finding a transition between order driven by conventional Fermi-surface nesting and order driven by Van Hove nesting. While the former describes an incommensurate Slater spin-density wave, the latter represents a Mott $(\pi,\pi)$ antiferromagnet, where the Fermi surface plays only a minor role. While most cuprates fall on the Slater-side of the transition, La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) lies just on the Mott side. Remarkably, just at the transition there is an emergent spin-liquid phase, which may play a role in the LSCO phase diagram.