Present status of the theory of high Tc cuprates

TL;DR

This paper reviews the Gutzwiller-projected mean field theory's role in understanding high-temperature cuprate superconductors, highlighting its successes, limitations, and fundamental differences from traditional many-body approaches.

Contribution

It explains the Gutzwiller-projected mean field theory and discusses its extensions and significance in describing cuprate phenomenology as a doped Mott insulator.

Findings

Successes in describing cuprate phenomenology

Fundamental differences from conventional perturbative theories

Potential extensions for improved understanding

Abstract

The Gutzwiller-projected mean field theory, also called Plain Vanilla or RMFT, is explained and its successes and possible extensions in describing the phenomenology of the cuprate superconductors are discussed. Throughout we emphasize that while this is a Hartree-Fock-BCS based theory, it embodies fundamental differences from conventional perturbative many-body theory which may be characterized by calling it a theory of the doped Mott insulator.