Mottness collapse and statistical quantum criticality

We put forward here the case that the anomalous electron states found in cuprate superconductors and related systems are rooted in a deeply non-classical fermion sign structure. The collapse of Mottness, as advocated by Phillips and supported by recent dynamical cluster approximation results on the Hubbard model, sets the necessary microscopic conditions. The crucial insight is due to Weng, who demonstrated that, in the presence of Mottness, the fundamental workings of quantum statistics change, and we will elaborate on the effects of this Weng statistics with an emphasis on characterizing it further using numerical methods. The pseudo-gap physics of the underdoped regime appears as a consequence of the altered statistics and the profound question is how to connect this by a continuous quantum phase transition to the overdoped regime ruled by normal Fermi–Dirac statistics. Proof of principle follows from Ceperley’s constrained path integral formalism, in which states can be explicitly constructed showing a merger of Fermi–Dirac sign structure and scale invariance of the quantum dynamics.