Mottness collapse and statistical quantum criticality

TL;DR

This paper explores how non-classical fermion sign structures, linked to Mottness collapse, influence anomalous electron states in cuprates, suggesting a quantum critical point connecting pseudogap and Fermi-liquid regimes.

Contribution

It introduces the concept of Weng statistics and demonstrates its role in the pseudogap physics and Mottness collapse using numerical methods and the constrained path integral formalism.

Findings

Mottness collapse sets conditions for anomalous states.

Weng statistics alters quantum behavior in Mott systems.

A continuous transition links pseudogap and Fermi-liquid regimes.

Abstract

We 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 DCA results on the Hubbard model is setting 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 changes and we will elaborate on the effects of this Weng statistics with an emphasis on characterizing these further using numerical methods. The pseudogap 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 where states can be explicitly constructed showing a merger of Fermi-Dirac sign structure and scale invariance of the quantum dynamics.