The project concerns theoretical, mainly numerical studies of the spectrum of the strongly correlated 2D electron gas. This non-perturbative approach is an attempt to contribute to the development of a predictive theory for e.g. high temperature superconductivity.
The first part of the project concerns diagonalization of the 2D Hubbard model for large lattices and many particles. The method is analytical construction of the projection operators corresponding to all known symmetries of the model followed by diagonalization of each invariant sub-space using standard numerical routines for smaller matrices and Tanczos algorithms for larger.
The second part concerns the analysis of spectra of the exact Hubbard model for various lattice sizes, particle numbers, and coupling strengths. Here the methods will be level statistics and comparison with approximative analytical models. A temperature will be introduced, and the level statistics will be done on energy levels weighted by their thermal occupation number.