315 research outputs found
Density Matrix Renormalization Group and the Nuclear Shell Model
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 . 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.Comment: 7 pages, 3 figures; To appears in Phys. Rev.
Exact solutions for pairing interactions
The exact solution of the BCS pairing Hamiltonian was found by Richardson in
1963. While little attention was paid to this exactly solvable model in the
remainder of the 20th century, there was a burst of work at the beginning of
this century focusing on its applications in different areas of quantum
physics. We review the history of this exact solution and discuss recent
developments related to the Richardson-Gaudin class of integrable models,
focussing on the role of these various models in nuclear physics.Comment: 14 pages, 2 figures, chapter in "Fifty Years of Nuclear BCS", eds.
R.A. Broglia and V.Zelevinsk
The Density Matrix Renormalization Group and the Nuclear Shell Model
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 Cr and 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
Structure of the number projected BCS wave function
We study the structure of the number projected BCS (PBCS) wave function in
the particle-hole basis, displaying its similarities with coupled clusters
theory (CCT). The analysis of PBCS together with several modifications
suggested by the CCT wave function is carried out for the exactly solvable
Richardson model involving a pure pairing hamiltonian acting in a space of
equally-spaced doubly-degenerate levels. We point out the limitations of PBCS
to describe the non-superconducting regime and suggest possible avenues for
improvement.Comment: 6 pages, 4 figures. To be published in Phys. Rev.
The Density Matrix Renormalization Group in Nuclear Physics: A Status Report
We report on the current status of recent efforts to develop the Density
Matrix Renormalization Group method for use in large-scale nuclear shell-model
calculations.Comment: 6 pages, 8 figures, Talk presented at the XXVI Symposium
on Nuclear Physics, 6 pages, 8 figures, Talk presented at the XXVIth
Symposium on Nuclear Physics,6-9 January 2003, Taxco, Mexic
Density Matrix Renormalization Group study of Cr and Ni
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 Ni and improved results for 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.Comment: 4 pages. Published in PRC Rapi
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