Mott physics, sign structure, ground state wavefunction, and high-T _c superconductivity

Abstract

In this article I give a pedagogical illustration of why the essential problem of high-T _c superconductivity in the cuprates is about how an antiferromagnetically ordered state can be turned into a short-range state by do**. I will start with half-filling where the antiferromagnetic ground state is accurately described by the Liang-Doucot-Anderson (LDA) wavefunction. Here the effect of the Fermi statistics becomes completely irrelevant due to the no double occupancy constraint. Upon do**, the statistical signs reemerge, albeit much reduced as compared to the original Fermi statistical signs. By precisely incorporating this altered statistical sign structure at finite do**, the LDA ground state can be recast into a short-range antiferromagnetic state. Superconducting phase coherence arises after the spin correlations become short-ranged, and the superconducting phase transition is controlled by spin excitations. I will stress that the pseudogap phenomenon naturally emerges as a crossover between the antiferromagnetic and superconducting phases. As a characteristic of non Fermi liquid, the mutual statistical interaction between the spin and charge degrees of freedom will reach a maximum in a high-temperature “strange metal phase” of the doped Mott insulator.