Phase transitions in partial summation methods: Results from the three-dimensional Hubbard model

The accurate determination of magnetic phase transitions in electronic systems is an important task of solidstate theory. While numerically exact results are readily available for model systems such as the half-filled 3D Hubbard model, the complexity of real materials requires additional approximations, such as the restriction to certain classes of diagrams in perturbation theory, that reduce the precision with which magnetic properties are described. In this paper, we examine the description of magnetic properties in second order perturbation theory, GW, fluctuation exchange, and two T-matrix approximations to numerically exact CT-QMC reference data. We assess finite-size effects and compare periodic lattice simulations to cluster embedding. We find that embedding substantially improves finite-size convergence. However, by analyzing different partial summation methods, we find no systematic improvement in the description of magnetic properties, with most methods considered in this paper predicting first-order instead of continuous transitions, leading us to the conclusion that nonperturbative methods are necessary for the accurate determination of magnetic properties and phase transitions.

Automated summary

The accurate determination of magnetic phase transitions in electronic systems is crucial but challenging. This paper examines various approximation methods and techniques to describe magnetic properties and phase transitions. The results suggest that nonperturbative methods are necessary for accurate determination.