Enhanced Diagrammatic Monte-Carlo Approaches for the Anisotropic Triangular Hubbard Model

In this thesis we first describe the implementation of our code base, which acts as a framework in which Diagrammatic Monte Carlo (DiagMC) is accessible for multiple different theories, at both the one- and two-particle propagator levels. We implement classical DiagMC along with the shifted-action approach, which offers improvements in convergence by expanding around an arbitrary starting point. Monte-Carlo updates are generalised for n-legged vertices, and for both standard and anomalous Green's functions. Observable classes are easily implemented and we offer the possibility of including global basis functions in the Monte-Carlo weight to reduce variance. Finally, we present benchmark data to confirm the validity of our implementation.

We then turn to an investigation of the evolution from the metallic to insulating state of the anisotropic triangular lattice Hubbard model, with motivations arising due to the rich physics found in this model, and the somewhat varied results found in the literature. Moreover, to the authors knowledge there is only one published study which applies DiagMC to the model. We present results for a number of observables at T = 0.5, for which we have used re-summation methods to extrapolate to infinite order. We find a smooth crossover from metallic to insulating state for all anisotropies studied, and the formation of 120◦ quasi-antiferromagnetic order in the isotropic limit.