Dynamical Correlation Functions using the Density Matrix Renormalization Group

The density matrix renormalization group (DMRG) method allows for very precise calculations of ground state properties in low-dimensional strongly correlated systems. We investigate two methods to expand the DMRG to calculations of dynamical properties. In the Lanczos vector method the DMRG basis is optimized to represent Lanczos vectors, which are then used to calculate the spectra. This method is fast and relatively easy to implement, but the accuracy at higher frequencies is limited. Alternatively, one can optimize the basis to represent a correction vector for a particular frequency. The correction vectors can be used to calculate the dynamical correlation functions at these frequencies with high accuracy. By separately calculating correction vectors at different frequencies, the dynamical correlation functions can be interpolated and pieced together from these results. For systems with open boundaries we discuss how to construct operators for specific wavevectors using filter functions.Comment: minor revision, 10 pages, 15 figure

The one-dimensional Bose-Hubbard Model with nearest-neighbor interaction

We study the one-dimensional Bose-Hubbard model using the Density-Matrix Renormalization Group (DMRG).For the cases of on-site interactions and additional nearest-neighbor interactions the phase boundaries of the Mott-insulators and charge density wave phases are determined. We find a direct phase transition between the charge density wave phase and the superfluid phase, and no supersolid or normal phases. In the presence of nearest-neighbor interaction the charge density wave phase is completely surrounded by a region in which the effective interactions in the superfluid phase are repulsive. It is known from Luttinger liquid theory that a single impurity causes the system to be insulating if the effective interactions are repulsive, and that an even bigger region of the superfluid phase is driven into a Bose-glass phase by any finite quenched disorder. We determine the boundaries of both regions in the phase diagram. The ac-conductivity in the superfluid phase in the attractive and the repulsive region is calculated, and a big superfluid stiffness is found in the attractive as well as the repulsive region.Comment: 19 pages, 30 figure