TOPOLOGICAL PROPERTIES OF THE SPIN-1 BOSE GAS IN THE HONEYCOMB LATTICE

Abstract

This thesis studies the (topological) properties of spin-1 Bosons in the honeycomb lattice in the presence of SU(3) spin-orbit coupling. For the non-interacting system, we study time reversal symmetry and topological properties of the spectrum and eigenstates. For broken time reversal symmetry, bulk bands have non-zero Chern numbers and chiral edge states develop in a lattice strip configuration. Transitions between different topological invariants are observed for varying chemical potentials. In the strongly interacting spin-1 Bose-Hubbard model, only the spin degrees of freedom are relevant. We determine ground-state and spin excitations via an effective Heisenberg model and mean-field approach on the spin-degrees of freedom. We find two antiferromagnetic-like phases that have well defined momentum space signatures and can be observed in cold atom experiments.