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Journal of Physics Conference Series

Extended application of the DMRG methodology to nuclei in the 1f– 2pshell

Stuart Pittel, B Thakur

Published Oct 31, 2011• 0 citations
Publisher

Abstract

In this paper, we present systematic results of the J-DMRG method (an angular-momentum-conserving version of the Density Matrix Renormalization Group) in truncated shell-model calculations of nuclei in the 1f – 2p shell. In contrast to earlier studies, these calculations consider both even-even and odd-mass nuclei. Comparison of the results of these calculations with those of exact shell-model treatments of the same nuclei shows that the method converges smoothly to the exact results in all cases and furthermore that the fraction of the full shell-model space required to obtain accurate agreement with the exact results decreases rapidly as the size of the full space grows. This latter result bodes well for the future applicability of the method to even larger nuclei with even larger shell-model spaces as is the ultimate goal of our development of this approach to large-scale shell model studies.

DOI
10.1088/1742-6596/322/1/012002

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In this paper, we present systematic results of the J-DMRG method (an angular-momentum-conserving version of the Density Matrix Renormalization Group) in truncated shell-model calculations of nuclei in the 1f – 2p shell. In contrast to earlier studies, these calculations consider both even-even and odd-mass nuclei. Comparison of the results of these calculations with those of exact shell-model treatments of the same nuclei shows that the method converges smoothly to the exact results in all cases and furthermore that the fraction of the full shell-model space required to obtain accurate agreement with the exact results decreases rapidly as the size of the full space grows. This latter result bodes well for the future applicability of the method to even larger nuclei with even larger shell-model spaces as is the ultimate goal of our development of this approach to large-scale shell model studies.
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.
We discuss the development of an angular-momentum-conserving variant of the Density Matrix Renormalization Group (DMRG) method for use in large-scale shell-model calculations of atomic nuclei and report a first application of the method to the ground state of 56Ni^{56}\mathrm{Ni}56Ni and improved results for 48Cr^{48}\mathrm{Cr}48Cr. In both cases, we see a high level of agreement with the exact results. A comparison of the two shows a dramatic reduction in the fraction of the space required to achieve accuracy as the size of the problem grows.
A new approach to large-scale nuclear structure calculations, based on the density matrix renormalization group (DMRG), is described. The DMRG method, which was developed originally in the framework of low-dimensional quantum lattices, has recently been extended to finite Fermi systems. Following a general description of this extended DMRG methodology, we briefly review its first application to a pairing hamiltonian. We then discuss its application to a schematic nuclear model involving many identical nucleons constrained to move in a single large-j shell. In those cases in which exact diagonalization of the hamiltonian is possible, the method is able to reproduce the exact results with extreme precision. Results are also presented for a model problem in which exact solution is not feasible.
"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."