Computational Methods for Shell-Model Calculations

Whitehead, R.R.; Watt, Alexander; Cole, B.J.; Morrison, I.

doi:10.1007/978-1-4615-8234-2_2

Cited by 181 publications

(121 citation statements)

References 23 publications

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“…by the Lanczos algorithm [26,27]. Within this framework I use two different model spaces and interactions.…”

Section: Methodsmentioning

confidence: 99%

“…I carry out the Lanczos algorithm with |Ψ as my pivot, that is the starting vector |v 1 : As is well-known for the Lanczos algorithm [27], this procedure generates a Krylov subspace and the eigenvalues of the tridiagonal matrix given by α i , β i will converge to the extremal eigenpairs ofL 2 , of which the eigenvectors are a linear combination of the Lanczos vectors,…”

Section: A L-s Decompositionmentioning

confidence: 99%

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Spin-orbit decomposition ofab initionuclear wave functions

Johnson

2015

Phys. Rev. C

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Although the modern shell-model picture of atomic nuclei is built from single-particle orbits with good total angular momentum j, leading to j-j coupling, decades ago phenomenological models suggested a simpler picture for 0p-shell nuclides can be realized via coupling of total spin S and total orbital angular momentum L. I revisit this idea with large-basis, no-core shell model (NCSM) calculations using modern ab initio two-body interactions, and dissect the resulting wavefunctions into their component L-and S-components. Remarkably, there is broad agreement with calculations using the phenomenological Cohen-Kurath forces, despite a gap of nearly fifty years and six orders of magnitude in basis dimensions. I suggest L-S decomposition may be a useful tool for analyzing ab initio wavefunctions of light nuclei, for example in the case of rotational bands.

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“…by the Lanczos algorithm [26,27]. Within this framework I use two different model spaces and interactions.…”

Section: Methodsmentioning

confidence: 99%

Section: A L-s Decompositionmentioning

confidence: 99%

Spin-orbit decomposition ofab initionuclear wave functions

Johnson

2015

Phys. Rev. C

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“…• Extension to larger ladders and systems of higher space dimensions with the help of more sophisticated numerical algorithms [27,28].…”

Section: Discussionmentioning

confidence: 99%

Study of the spectral properties of spin ladders in different representations via a renormalization procedure

Khalil

Richert

2011

Physica B: Condensed Matter

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“…Because one is generally interested only in low-lying states, typically the lowest 5-20 states, one can use Arnoldi methods such as the Lanczos algorithm [12,13], where one iteratively transforms the Hamiltonian to tridiagonal form:…”

Section: Introductionmentioning

confidence: 99%

“…the extremal eigenvalues converge quickly [13], which one can understand through the lens of the classical moments problem [14]. The downside of Lanczos is that, due to numerical round-off error the Lanczos vectors |v n lose orthogonality and must be forcibly orthonormalized, which is why Householder is often preferred when one must completely transform a matrix to tridiagonal form.…”

Section: Introductionmentioning

confidence: 99%

Factorization in large-scale many-body calculations

Johnson

Ormand

Krastev

2013

Computer Physics Communications

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One approach for solving interacting many-fermion systems is the configurationinteraction method, also sometimes called the interacting shell model, where one finds eigenvalues of the Hamiltonian in a many-body basis of Slater determinants (antisymmetrized products of single-particle wavefunctions). The resulting Hamiltonian matrix is typically very sparse, but for large systems the nonzero matrix elements can nonetheless require terabytes or more of storage. An alternate algorithm, applicable to a broad class of systems with symmetry, in our case rotational invariance, is to exactly factorize both the basis and the interaction using additive/multiplicative quantum numbers; such an algorithm recreates the many-body matrix elements on the fly and can reduce the storage requirements by an order of magnitude or more. We discuss factorization in general and introduce a novel, generalized factorization method, essentially a 'double-factorization' which speeds up basis generation and set-up of required arrays. Although we emphasize techniques, we also place factorization in the context of a specific (unpublished) configuration-interaction code, BIGSTICK, which runs both on serial and parallel machines, and discuss the savings in memory due to factorization.

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Computational Methods for Shell-Model Calculations

Cited by 181 publications

References 23 publications

Spin-orbit decomposition ofab initionuclear wave functions

Spin-orbit decomposition ofab initionuclear wave functions

Study of the spectral properties of spin ladders in different representations via a renormalization procedure

Factorization in large-scale many-body calculations

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