Dual Fermions Study of the 2D Hubbard Model

Sergei Iskakov, Emanuel Gull

Fedor vSimkovic, Evgeny Kozik, Boris V. Svistunov +2 more

Behnam Arzhang

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.

Jamie R. Williams, Thomas Essinger-Hileman, R.W. Stites +1 more

Joseph Paki

This thesis will describe efforts to enhance our ability to simulate the 2D Hubbard model. Chapter 2 provides a background on the main computational techniques used throughout the work, including quantum Monte Carlo (QMC), dynamical mean field theory (DMFT), the dynamical cluster approximation (DCA), the continuous time auxiliary field algorithm (CTAUX), and the Maximum Entropy Method (MEM) for numeric analytic continuation. Chapter 3 presents new work on applying Twisted Boundary Conditions to the DCA framework. This method is applied in a effort to access thermodynamic (i.e. large system) information about the Hubbard model without the immense computational expense required to simulate large lattices directly. Chapter 4 describes efforts to study the extended 2D Hubbard model, which re-introduces non-local interactions between electrons that drive the formation of charge ordered phases. The work includes a thorough analysis of the phase diagram of the model away from half-filling, as well as analysis of the effect of non-local interactions on anti-ferromagnetic fluctuations and competition between the charge order and AFM states. Chapter 5 includes a derivation of the dual fermions diagrammatic expansion and the dual fermions ladder approximation used to compute corrections to single site DMFT calculations. The method is applied to the 2D Hubbard model in order to study the evolution of its spectral function, Fermi surface, and momentum dependent mass renormalization as the temperature, interaction strength, and doping are changed. The great advantage of this method is that we are able to access arbitrary momenta throughout the Brillouin zone, in contrast to the limitation to a few cluster momenta that characterize cluster methods like DCA.

Michael Köhl