Electronic correlations in the Hubbard model on a bi-partite lattice

In this work we study the Hubbard model on a bi-partite lattice using the coupled-cluster method (CCM). We first investigate how to implement this approach in order to reproduce the lack of magnetic order in the 1D model, as predicted by the exact Bethe-Ansatz solution. This result can only be reproduced if we include an algebraic correlation in some of the coupled-cluster model coefficients. Using the correspondence between the Heisenberg model and the Hubbard model in the large-coupling limit, we use very accurate results for the CCM applied to the Heisenberg and its generalisation, the XXZ model, to determine CCM coefficients with the correct properties. Using the same approach we then study the 2D Hubbard model on a square and a honeycomb lattice, both of which can be thought of as simplified models of real 2D materials. We analyse the charge and spin excitations, and show that with care we can obtain good results.