Gutzwiller Magnetic Phase Diagram of the Cuprates

TL;DR

This paper develops a method to analyze magnetic instabilities in two-dimensional materials, applying it to the Hubbard model for cuprates, revealing doping-dependent magnetic interactions and the influence of different theoretical approximations.

Contribution

It introduces a constructive procedure for analyzing magnetic instabilities using double nesting, applied to Gutzwiller and Hartree-Fock methods for the Hubbard model.

Findings

Magnetic interactions in cuprates are present only for hole doping.

Hartree-Fock+RPA predicts instabilities across all dopings with large U.

Gutzwiller approximation restricts instabilities to doping ranges relevant for cuprates.

Abstract

A general constructive procedure is presented for analyzing magnetic instabilities in two-dimensional materials, in terms of [predominantly] double nesting, and applied to Hartree-Fock HF+RPA and Gutzwiller approximation GA+RPA calculations of the Hubbard model. Applied to the cuprates, it is found that competing magnetic interactions are present only for hole doping, between half filling and the Van Hove singularity. While HF+RPA instabilities are present at all dopings (for sufficiently large Hubbard U), in a Gutzwiller approximation they are restricted to a doping range close to the range of relevance for the physical cuprates. The same model would hold for charge instabilities, except that the interaction is more likely to be q-dependent.