Efficient calculation of the antiferromagnetic phase diagram of the 3D Hubbard model

TL;DR

This paper employs the Dynamical Cluster Approximation with Betts clusters to efficiently compute the antiferromagnetic phase diagram of the 3D Hubbard model at half filling, achieving accurate results with significantly smaller clusters.

Contribution

It introduces the use of Betts clusters within the DCA framework for the 3D Hubbard model, enabling accurate phase diagram calculations with fewer computational resources.

Findings

Qualitative agreement with previous studies.

Smaller clusters (48 vs. 1000) suffice for accurate results.

Systematic finite-size scaling confirms the method's effectiveness.

Abstract

The Dynamical Cluster Approximation with Betts clusters is used to calculate the antiferromagnetic phase diagram of the 3D Hubbard model at half filling. Betts clusters are a set of periodic clusters which best reflect the properties of the lattice in the thermodynamic limit and provide an optimal finite-size scaling as a function of cluster size. Using a systematic finite-size scaling as a function of cluster space-time dimensions, we calculate the antiferromagnetic phase diagram. Our results are qualitatively consistent with the results of Staudt et al. [Eur. Phys. J. B 17 411 (2000)], but require the use of much smaller clusters: 48 compared to 1000.