Fluctuation diagnostics in the 2D Hubbard model from the dual-fermion method

Arzhang, Behnam (2019) Fluctuation diagnostics in the 2D Hubbard model from the dual-fermion method. Masters thesis, Memorial University of Newfoundland.

[English] PDF - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. Download (6MB)

Abstract

In this thesis, we use the Dual Fermion approximation (DF) to study the Hubbard model on the 2D square lattice by using two-particle quantities such as susceptibilities and full vertex functions. In the first chapter we give an introduction to the strongly correlated systems including their definitions and features. Then, in the next chapter, to solve our model we present some numerical methods. The numerical methods that we used for our study are the dynamical mean-field theory (DMFT), the continuous-time auxiliary field impurity solver (CTAUX), Fluctuation diagnostics and Dual Fermion approximation (DF). The DF method provides high-resolution results for single-particle quantities such as the density of states (DOS) and Self Energy as well two particles spin susceptibility and vertex functions. With these results, we can present high-resolution results of the fluctuation diagnostics method with minimal computational expense. We examine the full Q-vector dependence of the extended self-energy at the Nodal and Antinodal k-points and provide interpretation for the claim that spin fluctuations are responsible for the observed metal-to-insulator behaviour.

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