Least-square approach for singular value decompositions of scattering problems

Abstract

It was recently observed that chiral two-body interactions can be efficiently represented using matrix factorization techniques such as the singular value decomposition. However, the exploitation of these low-rank structures in a few- or many-body framework is nontrivial and requires reformulations that explicitly utilize the decomposition format. In this work, we present a general least-square approach that is applicable to different few- and many-body frameworks and allows for an efficient reduction to a low number of singular values in the least-square iteration. We verify the feasibility of the least-square approach by solving the Lippmann-Schwinger equation in factorized form. The resulting low-rank approximations of the $T$ matrix are found to fully capture scattering observables. Potential applications of the least-square approach to other frameworks with the goal of employing tensor factorization techniques are discussed.

arXiv comment8 pages, 4 figures, 1 table, version accepted at Phys. Rev. C

References in corpus (55)

• The density-matrix renormalization group in the age of matrix product states
• Modern Theory of Nuclear Forces
• Chiral effective field theory and nuclear forces
• Improved nuclear matter calculations from chiral low-momentum interactions
• Coupled-cluster computations of atomic nuclei
• Self-consistent Green's function method for nuclei and nuclear matter
• Accurate nuclear radii and binding energies from a chiral interaction
• The In-Medium Similarity Renormalization Group: A Novel Ab Initio Method for Nuclei
• Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order
• High-quality two-nucleon potentials up to fifth order of the chiral expansion
• Chiral interactions up to next-to-next-to-next-to-leading order and nuclear saturation
• The Density Matrix Renormalization Group in Chemistry and Molecular Physics: Recent Developments and New Challenges
• Quantifying truncation errors in effective field theory
• A Guided Tour of Ab Initio Nuclear Many-Body Theory
• Ab initio predictions link the neutron skin of ${}^{208}$Pb to nuclear forces
• Non-Empirical Interactions for the Nuclear Shell Model: An Update
• Structure of the lightest tin isotopes
• Ab initio limits of atomic nuclei
• Importance Truncation for Large-Scale Configuration Interaction Approaches
• Ab Initio Path to Heavy Nuclei
• Novel chiral Hamiltonian and observables in light and medium-mass nuclei
• Accurate bulk properties of nuclei from $A=2$ to $\infty$ from potentials with $\Delta$ isobars
• Three-Nucleon Forces: Implementation and Applications to Atomic Nuclei and Dense Matter
• Converged ab initio calculations of heavy nuclei
• Symmetric nuclear matter with chiral three-nucleon forces in the self-consistent Green's functions approach
• Charge radii of exotic neon and magnesium isotopes
• Three-nucleon forces and spectroscopy of neutron-rich calcium isotopes
• Bogoliubov Many-Body Perturbation Theory for Open-Shell Nuclei
• Few- and many-nucleon systems with semilocal coordinate-space regularized chiral two- and three-body forces
• Hartree-Fock Many-Body Perturbation Theory for Nuclear Ground-States
• Fitting theories of nuclear binding energies
• Microscopically-based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization
• Angular-momentum projection in coupled-cluster theory: structure of ${}^{34}$Mg
• Can tetraneutron be a narrow resonance?
• In-medium similarity renormalization group with three-body operators
• Emergent properties of nuclei from ab initio coupled-cluster calculations
• Multi-reference many-body perturbation theory for nuclei III -- Ab initio calculations at second order in PGCM-PT
• Tensor-Structured Coupled Cluster Theory
• Ab initio computation of charge densities for Sn and Xe isotopes
• Advanced density matrix renormalization group method for nuclear structure calculations
• Natural orbitals for ab initio no-core shell model calculations
• Rank-reduced coupled-cluster III. Tensor hypercontraction of the doubles amplitudes
• Combining the in-medium similarity renormalization group with the density matrix renormalization group: Shell structure and information entropy
• Natural orbitals for many-body expansion methods
• Density matrix renormalization group and wave function factorization for nuclei
• Pre-processing the nuclear many-body problem: Importance truncation versus tensor factorization techniques
• Tensor-decomposition techniques for ab initio nuclear structure calculations. From chiral nuclear potentials to ground-state energies
• Deformed in-medium similarity renormalization group
• Gorkov algebraic diagrammatic construction formalism at third order
• Natural orbitals for the ab initio no-core configuration interaction approach
• Low-rank matrix decompositions for ab initio nuclear structure
• Importance truncation in non-perturbative many-body techniques
• Importance truncation for the in-medium similarity renormalization group
• Model space truncation in shell-model fits
• Sensitivity analysis of random two-body interactions

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