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arXiv:nucl-th/0601044 · Physical Review C

Density matrix renormalization group and the nuclear shell model

Stuart Pittel, Nicolae Sandulescu

Published Jan 17, 2006• 34 citations
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Abstract

We describe the use of the density matrix renormalization group method as a means of approximately solving large-scale nuclear shell-model problems. We focus on an angular-momentum-conserving variant of the method and report test results for the nucleus $^{48}\mathrm{Cr}$. The calculation is able to reproduce both the ground-state energy and the energy of the first excited state, by diagonalizing matrices much smaller than those of the full shell model.

DOI
10.1103/physrevc.73.014301

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We describe the use of the density matrix renormalization group method as a means of approximately solving large-scale nuclear shell-model problems. We focus on an angular-momentum-conserving variant of the method and report test results for the nucleus 48Cr^{48}\mathrm{Cr}48Cr. The calculation is able to reproduce both the ground-state energy and the energy of the first excited state, by diagonalizing matrices much smaller than those of the full shell model.
"We briefly review the Density Matrix Renormalization Group (DMRG) method and its potential use in large-scale nuclear shell-model calculations. We propose the use of an angular-momentum-conserving variant of the method (the JDMRG) and report the first test results of such an approach for the nucleus 48 Cr. The positive results of these calculations have motivated us to search for an even more efficient means of implementing the JDMRG strategy and the status of these efforts is also described."
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We summarize our recent efforts to develop the Density Matrix Renormalization Group (DMRG) method into a practical truncation strategy for large-scale nuclear shell model calculations. Following an overview of the essential features of the DMRG, we discuss the changes we have implemented for its use in nuclei. In particular, we have found it useful to develop an angular-momentum conserving variant of the method (the JDMRG). We then summarize the principal results we have obtained to date, first reporting test results for 48^{48}48Cr and then more recent test results for 56^{56}56Ni. In both cases we consider nucleons limited to the 2p-1f shell. While both calculations produce a high level of agreement with the exact shell model results, the fraction of the complete space required to achieve this high level of agreement is found to go down rapidly as the size of the full space grows.
We summarize recent efforts to develop an angular-momentum-conserving variant of the Density Matrix Renormalization Group method into a practical truncation strategy for large-scale shell model calculations of atomic nuclei. Following a brief description of the key elements of the method, we report the results of test calculations for 48 Cr and 56 Ni . In both cases we consider nucleons limited to the 2p-1f shell and interacting via the KB3 interaction. Both calculations produce a high level of agreement with the exact shell-model results. Furthermore, and most importantly, the fraction of the complete space required to achieve this high level of agreement goes down rapidly as the size of the full space grows.
A new approach to large-scale nuclear structure calculations, based on the density matrix renormalization group (DMRG), is described. The method is tested in the context of a problem involving many identical nucleons constrained to move in a single large-jjj shell and interacting via a pairing plus quadrupole interaction. In cases in which exact diagonalization of the Hamiltonian is possible, the method is able to reproduce the exact results for the ground-state energy and the energies of low-lying excited states with extreme precision. Results are also presented for a model problem in which exact solution is not feasible.