Strongly Correlated Phases in the Anisotropic Honeycomb Lattice

Abstract

In this thesis we present our results concerning the various strongly correlated phases and phase transitions in the honeycomb optical lattice with in-plane anisotropic hopping amplitudes. In particular, the anti-ferromagnetic and the spin-liquid transition in the monolayer honeycomb lattice as well as the pairing transition in the AA-stacked bilayer case are studied, both within the framework of the Hubbard Model. The main methods used are the mean-field self-consistent and the slave-rotor methods. The results of these methods are then complemented by the Stoner?s criterion calculation and an effective Hamiltonian that we derived for the strongly-correlated limit. The AF transition line that we obtained shows features that can be explained using simple physical arguments, while our studies on the possible spin-liquid phase provide convincing arguments for the existence of a spin-liquid phase in the limit of strong-anisotropy.