Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Revista Mexicana de Física

The density matrix renormalization group and nuclear structure

Stuart Pittel, B Thakur, Nicolae Sandulescu

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

"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."

Related papers

The Density Matrix Renormalization Group and the Shell Model

Stuart Pittel, B Thakur

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 $^{48}$Cr and then more recent test results for $^{56}$Ni. 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.

arXiv:0904.2345•Apr 15, 2009•0 citations

Density matrix renormalization group and the nuclear shell model

Stuart Pittel, Nicolae Sandulescu

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.

arXiv:nucl-th/0601044•Physical Review C•Jan 17, 2006•34 citations

Density matrix renormalization group study of Cr 48 and Ni 56

B Thakur, Stuart Pittel, Nicolae Sandulescu

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 $^{56}\mathrm{Ni}$ and improved results for $^{48}\mathrm{Cr}$. 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.

arXiv:0808.1277•Physical Review C•Oct 20, 2008•30 citations

The Density Matrix Renormalization Group and Nuclear Structure

Stuart Pittel

We briefly review the key features of the Density Matrix Renormalization Group method, focusing on its potential use in solving large‐scale nuclear shell‐model problems. A test application of an angular‐momentum‐conserving variant of the method in 48Cr shows its great promise.

AIP conference proceedings•Jan 1, 2006•0 citations

THE DENSITY MATRIX RENORMALIZATION GROUP AND THE NUCLEAR SHELL MODEL

Stuart Pittel, B Thakur, Nicolae Sandulescu

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.

arXiv:0808.1303•International Journal of Modern Physics E•Dec 1, 2008•2 citations

The density matrix renormalization group: a new approach to large-scale nuclear structure calculations

Stuart Pittel, J. Dukelsky

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.

Revista Mexicana de Física•Jan 1, 2001•0 citations
"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."
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 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 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.
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 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.