Extracting Infinite System Properties from Finite Size Clusters: Phase Randomization/Boundary Condition Averaging

When electron-electron correlations are important, it is often necessary to use exact numerical methods, such as Lanczos diagonalization, to study the full many-body Hamiltonian. Unfortunately, such exact diagonalization methods are restricted to small system sizes. We show that if the Hubbard U term is replaced by a periodic Hubbard term, the full many body Hamiltonian may be exactly solved, even for very large systems, though for low fillings. However, for half-filled systems and large U this approach is not only no longer exact, it no longer improves extrapolation to larger systems. We discuss how generalized randomized variable averaging RVA or phase randomization schemes can be reliably employed to improve extrapolation to large system sizes in this regime. This general approach can be combined with any many-body method and is thus of broad interest and applicability.... Randomized variable averaging RVA , Extrapolation.