Development of a dual fermion approach to the fcc Hubbard model

Thesis

We develop a codebase for performing dynamical mean field theory (DMFT) and dual fermion (DF) calculations on the Hubbard model, by modifying, extending, and interfacing several pre-existing open-source codes. This is used to examine the Hubbard model on a face-centered cubic (fcc) lattice, to obtain numerically-exact results at the level of DMFT and investigate the effect of non-local electron correlations within the dual fermion approach.

Our code centres around a modified implementation of the CTHYB quantum Monte Carlo technique used as an impurity solver. We discuss the modifications made, and validate our code by comparing its results to known results in the literature. The DF calculations are obtained by using the CTHYB results as inputs to an extension of the OpenDF code, which we likewise validate by comparison of our results to those of previous authors.

We study the magnetic phase diagram, magnetic susceptibilities, and single-particle dynamics of the Hubbard model on the fcc lattice. Within DMFT a large FM region is found above half-filling, the phase boundary of which is located precisely by susceptibility and magnetisation calculations. A large AFM phase is found around and below half-filling with contributions from instabilities towards the X and W points. Single-particle spectra are obtained using the Maximum Entropy method for a wide range of temperatures and fillings demonstrating how the spectra change as the FM phase boundary is crossed.

The non-local correlations taken into account by the DF approach reduce the critical temperatures of both the FM and AFM regions. Corrections in the FM region are small and strongly suggest that DMFT is able to capture the relevant physics in this region of the phase diagram.

The code developed as part of this project opens the door for further investigations of the Hubbard model on the fcc, and other lattices, across wide ranges of parameter space.

Authors: Howell, M

• DOI: 10.5287/ora-gaqoervv9
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: dual fermion; CT-QMC; magnetism; DMFT
• Subjects: Condensed matter