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Title: Unitary correlation operator method from a similarity renormalization group perspective

Abstract

We investigate how the unitary correlation operator method (UCOM), developed to explicitly describe the strong short-range central and tensor correlations present in the nuclear many-body system, relates to the similarity renormalization group (SRG), a method to band-diagonalize Hamiltonians by continuous unitary transformations. We demonstrate that the structure of the UCOM transformation, originally motivated from the physically intuitive picture of correlations in coordinate space, arises naturally from the SRG flow equation. Apart from formal considerations we show that the momentum space matrix elements of the effective interactions obtained in both schemes agree extremely well.

Authors:
;  [1]
  1. Institut fuer Kernphysik, Technische Universitaet Darmstadt, D-64289 Darmstadt (Germany)
Publication Date:
OSTI Identifier:
20995253
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. C, Nuclear Physics; Journal Volume: 75; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevC.75.051001; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRELATIONS; EQUATIONS; HAMILTONIANS; INTERACTIONS; MANY-BODY PROBLEM; MATRIX ELEMENTS; RENORMALIZATION; TENSORS

Citation Formats

Hergert, H., and Roth, R. Unitary correlation operator method from a similarity renormalization group perspective. United States: N. p., 2007. Web. doi:10.1103/PHYSREVC.75.051001.
Hergert, H., & Roth, R. Unitary correlation operator method from a similarity renormalization group perspective. United States. doi:10.1103/PHYSREVC.75.051001.
Hergert, H., and Roth, R. Tue . "Unitary correlation operator method from a similarity renormalization group perspective". United States. doi:10.1103/PHYSREVC.75.051001.
@article{osti_20995253,
title = {Unitary correlation operator method from a similarity renormalization group perspective},
author = {Hergert, H. and Roth, R.},
abstractNote = {We investigate how the unitary correlation operator method (UCOM), developed to explicitly describe the strong short-range central and tensor correlations present in the nuclear many-body system, relates to the similarity renormalization group (SRG), a method to band-diagonalize Hamiltonians by continuous unitary transformations. We demonstrate that the structure of the UCOM transformation, originally motivated from the physically intuitive picture of correlations in coordinate space, arises naturally from the SRG flow equation. Apart from formal considerations we show that the momentum space matrix elements of the effective interactions obtained in both schemes agree extremely well.},
doi = {10.1103/PHYSREVC.75.051001},
journal = {Physical Review. C, Nuclear Physics},
number = 5,
volume = 75,
place = {United States},
year = {Tue May 15 00:00:00 EDT 2007},
month = {Tue May 15 00:00:00 EDT 2007}
}
  • We discuss relations and differences between two methods for the construction of unitarily transformed effective interactions, the Similarity Renormalization Group (SRG) and Unitary Correlation Operator Method (UCOM). The aim of both methods is to construct a soft phase-shift equivalent effective interaction which is well suited for many-body calculations in limited model spaces. After contrasting the two conceptual frameworks, we establish a formal connection between the initial SRG-generator and the static generators of the UCOM transformation. Furthermore we propose a mapping procedure to extract UCOM correlation functions from the SRG evolution. We compare the effective interactions resulting from the UCOM-transformation andmore » the SRG-evolution on the level of matrix elements, in no-core shell model calculations of light nuclei, and in Hartree-Fock calculations up to {sup 208}Pb. Both interactions exhibit very similar convergence properties in light nuclei but show a different systematic behavior as function of particle number.« less
  • Similarity renormalization group (SRG) flow equations can be used to unitarily soften nuclear Hamiltonians by decoupling high-energy intermediate-state contributions to low-energy observables while maintaining the natural hierarchy of many-body forces. Analogous flow equations can be used to consistently evolve operators so that observables are unchanged if no approximations are made. The question in practice is whether the advantages of a softer Hamiltonian and less-correlated wave functions might be offset by complications in approximating and applying other operators. Here we examine the properties of SRG-evolved operators, focusing in this article on applications to the deuteron but leading toward methods for few-bodymore » systems. We find the advantageous features generally carry over to other operators with additional simplifications in some cases from factorization of the unitary transformation operator.« less
  • Research Highlights: > We study the similarity renormalization group evolution of chiral NN potentials. > We evolve an effective potential derived using a subtractive renormalization scheme. > Unitarity of the SRG evolution is verified within the subtractive scheme. > High- and low-momentum components decouple for the SRG evolved potential. - Abstract: Methods based on Wilson's renormalization group have been successfully applied in the context of nuclear physics to analyze the scale dependence of effective nucleon-nucleon (NN) potentials, as well as to consistently integrate out the high-momentum components of phenomenological high-precision NN potentials in order to derive phase-shift equivalent softer forms,more » the so called V{sub low-k} potentials. An alternative renormalization group approach that has been applied in this context is the similarity renormalization group (SRG), which is based on a series of continuous unitary transformations that evolve hamiltonians with a cutoff on energy differences. In this work we study the SRG evolution of a leading order (LO) chiral effective NN potential in the {sup 1}S{sub 0} channel derived within the framework of the subtracted kernel method (SKM), a renormalization scheme based on a subtracted scattering equation.« less
  • We have developed a fully consistent framework for calculations in the quasiparticle random-phase approximation (QRPA) with NN interactions from the Similarity Renormalization Group (SRG) and other unitary transformations of realistic interactions. The consistency of our calculations, which use the same Hamiltonian to determine the Hartree-Fock-Bogoliubov ground states and the residual interaction for QRPA, guarantees an excellent decoupling of spurious strength, without the need for empirical corrections. While work is under way to include SRG-evolved 3N interactions, we presently account for some 3N effects by means of a linearly density-dependent interaction, whose strength is adjusted to reproduce the charge radii ofmore » closed-shell nuclei across the whole nuclear chart. As a first application, we perform a survey of the monopole, dipole, and quadrupole response of the calcium isotopic chain and of the underlying single-particle spectra, focusing on how their properties depend on the SRG parameter {lambda}. Unrealistic spin-orbit splittings suggest that spin-orbit terms from the 3N interaction are called for. Nevertheless, our general findings are comparable to results from phenomenological QRPA calculations using Skyrme or Gogny energy density functionals. Potentially interesting phenomena related to low-lying strength warrant more systematic investigations in the future.« less