Phase transitions in partial summation methods: Results from the 3D Hubbard model

TL;DR

This study evaluates various perturbation theory methods for predicting magnetic phase transitions in the 3D Hubbard model, revealing their limitations and emphasizing the need for non-perturbative approaches for accuracy.

Contribution

The paper systematically compares partial summation methods to numerically exact data, highlighting their inability to reliably predict the nature of magnetic phase transitions.

Findings

Embedding improves finite-size convergence.

Most methods predict first-order transitions instead of continuous.

Non-perturbative methods are necessary for accurate phase transition analysis.

Abstract

The accurate determination of magnetic phase transitions in electronic systems is an important task of solid state 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 work, we examine the description of magnetic properties in second order perturbation theory, GW, FLEX, and two TMatrix 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 work predicting first-order instead of continuous transitions, leading us to the conclusion that non-perturbative methods are necessary for the accurate determination of magnetic properties and phase transitions.