Magnetism in the Hubbard model-An improved treatment

TL;DR

This paper introduces a hybrid tau-CPA method combining CPA and VCA to better predict magnetic ordering in the Hubbard model, addressing limitations of previous approaches.

Contribution

A novel hybrid tau-CPA approach that improves magnetic predictions in the Hubbard model by integrating CPA and VCA techniques.

Findings

Predicts magnetism using a modified Stoner criterion

Addresses limitations of CPA in predicting magnetic ground states

Provides a more accurate treatment of electron scattering and magnetism

Abstract

We propose a new treatment of the Hubbard model that is based both on the coherent-potential approximation (CPA) and the virtual-crystal approximation (VCA). It is well known that the equilibrium found using the one-particle CPA Green's functions does not predict an ordered magnetic ground state, while Stoner's mean-field treatment, which is equivalent to the VCA on the Hubbard model, does so for a wide range of parameters. A hybrid treatment, the tau-CPA, is developed, in which a particle is assumed to be scattered from an array of static opposite spins for a time tau related to the inverse of the band width. The propagation is treated in the CPA over this period; thereafter the particle sees the time-averaged effect of the scatterers and hence can be treated in the VCA. This model, with suitable approximations, does predict magnetism for a modified Stoner criterion.