Density matrix renormalization group approach for large scale nuclear structure calculations

The Nuclear Shell Model(SM) lies at the heart of a large number of microscopic investigations in theoretical nuclear structure physics, especially concerning medium-mass nuclei. The challenge in carrying out SM-based calculations comes from the size of the valence space, which grows exponentially with increasing nucleon-number and with larger single particle orbitals. As a result, exact diagonalization methods are impractical for most medium and larger mass nuclei. This has led to the fertile development of methods aimed at providing a further truncation of the SM space. The Density Matrix Renormalization Group (DMRG) method has had outstanding success in similar fields where exact diagonalization in the full model space is not possible. This dissertation is an attempt to use DMRG for carrying out SM-based large-scale nuclear structure calculations. The method has been tailored to accommodate the peculiarities of the nuclear problem. We have performed calculations for a wide variety of nuclei in the 1f-2p shell for which exact diagonalization is possible, with the goal being to see how well the method works. The analysis was carried out for both even-even and odd-mass nuclei. We considered nuclei with increasing valence space dimensions to test the scalability of the procedure. The results show that DMRG can replicate the exact SM results to good accuracy for both even and odd-mass nuclei, using only a small fraction of the valence space and furthermore that the fraction required to get good accuracy goes down very rapidly with increasing valence space dimensions. This is very encouraging for future applications to even larger nuclei where exact SM calculations are not yet and may never be possible. For somewhat heavier nuclei in the 1f-2p shell nuclei, it becomes important to include the effects of the intruding 1g9/2 orbital and methods to treat such large orbitals, as are also relevant to even heavier nuclei, have been discussed. A prescription for treating important observables other than energies has also been presented. Overall, we find the method to be very robust and capable of providing a good approximation to exact SM calculations.