Background: The newly developed selfconsistent GorkovGreen's function approach represents a promising path to the ab initio description of midmass openshell nuclei. The formalism based on a twonucleon interaction and the secondorder truncation of Gorkov's selfenergy has been described in detail in Ref. [Somà, Duguet, and Barbieri, Phys. Rev. C 84, 064317 (2011)PRVCAN0556281310.1103/PhysRevC.84.064317]. Purpose: The objective is to discuss the methodology used to solve Gorkov's equation numerically and to gauge its performance in view of carrying out systematic calculations of mediummass nuclei in the future. In doing so, different sources of theoretical error and degrees of selfconsistency are investigated. Methods: We employ Krylov projection techniques with a multipivot Lanczos algorithm to efficiently handle the growth of poles in the onebody Green's function that arises as a result of solving Gorkov's equation selfconsistently. We first characterize the numerical scaling of Gorkov's calculations based on full selfconsistency and on a partially selfconsistent scheme coined as "sc0". Using small model spaces, the Krylov projection technique is then benchmarked against exact diagonalization of the original Gorkov matrix. Next, the convergence of the results as a function of the number Nℓ of Lanczos iterations per pivot is investigated in large model spaces. Eventually, the convergence of the calculations with the size of the harmonic oscillator model space is examined. Results: Gorkov selfconsistent Green's function (SCGF) calculations performed on the basis of Krylov projection techniques display a favorable numerical scaling that authorizes systematic calculations of midmass nuclei. The Krylov projection selects efficiently the appropriate degrees of freedom while spanning a very small fraction of the original space. For typical largescale calculations of midmass nuclei, a Krylov projection making use of Nℓ≈50 yields a sufficient degree of accuracy on the observables of interest. The partially selfconsistent sc0 scheme is shown to reproduce fully selfconsistent solutions in small model spaces at the 1% level. Eventually, GorkovGreen's function calculations performed on the basis of SRGevolved interactions show a fast convergence as a function of the modelspace size. Conclusions: The end result is a tractable, accurate and gently scaling ab initio scheme applicable to complete isotopic and isotonic chains in the mediummass region. The partially selfconsistent sc0 scheme provides an excellent compromise between accuracy and computational feasibility and will be the workhorse of systematic GorkovGreen's function calculations in the future. The numerical scaling and performances of the algorithm employed offers the possibility (i) to apply the method to even heavier systems than those (e.g., 74Ni) already studied so far and (ii) to perform converged Gorkov SCGF calculations based on harder, e.g. original chiral interactions.
Ab initio selfconsistent GorkovGreen's function calculations of semimagic nuclei: Numerical implementation at second order with a twonucleon interaction / V. Soma, C. Barbieri, T. Duguet.  In: PHYSICAL REVIEW. C, NUCLEAR PHYSICS.  ISSN 05562813.  89:2(2014), pp. 024323.1024323.16. [10.1103/PhysRevC.89.024323]
Ab initio selfconsistent GorkovGreen's function calculations of semimagic nuclei: Numerical implementation at second order with a twonucleon interaction
C. Barbieri;
2014
Abstract
Background: The newly developed selfconsistent GorkovGreen's function approach represents a promising path to the ab initio description of midmass openshell nuclei. The formalism based on a twonucleon interaction and the secondorder truncation of Gorkov's selfenergy has been described in detail in Ref. [Somà, Duguet, and Barbieri, Phys. Rev. C 84, 064317 (2011)PRVCAN0556281310.1103/PhysRevC.84.064317]. Purpose: The objective is to discuss the methodology used to solve Gorkov's equation numerically and to gauge its performance in view of carrying out systematic calculations of mediummass nuclei in the future. In doing so, different sources of theoretical error and degrees of selfconsistency are investigated. Methods: We employ Krylov projection techniques with a multipivot Lanczos algorithm to efficiently handle the growth of poles in the onebody Green's function that arises as a result of solving Gorkov's equation selfconsistently. We first characterize the numerical scaling of Gorkov's calculations based on full selfconsistency and on a partially selfconsistent scheme coined as "sc0". Using small model spaces, the Krylov projection technique is then benchmarked against exact diagonalization of the original Gorkov matrix. Next, the convergence of the results as a function of the number Nℓ of Lanczos iterations per pivot is investigated in large model spaces. Eventually, the convergence of the calculations with the size of the harmonic oscillator model space is examined. Results: Gorkov selfconsistent Green's function (SCGF) calculations performed on the basis of Krylov projection techniques display a favorable numerical scaling that authorizes systematic calculations of midmass nuclei. The Krylov projection selects efficiently the appropriate degrees of freedom while spanning a very small fraction of the original space. For typical largescale calculations of midmass nuclei, a Krylov projection making use of Nℓ≈50 yields a sufficient degree of accuracy on the observables of interest. The partially selfconsistent sc0 scheme is shown to reproduce fully selfconsistent solutions in small model spaces at the 1% level. Eventually, GorkovGreen's function calculations performed on the basis of SRGevolved interactions show a fast convergence as a function of the modelspace size. Conclusions: The end result is a tractable, accurate and gently scaling ab initio scheme applicable to complete isotopic and isotonic chains in the mediummass region. The partially selfconsistent sc0 scheme provides an excellent compromise between accuracy and computational feasibility and will be the workhorse of systematic GorkovGreen's function calculations in the future. The numerical scaling and performances of the algorithm employed offers the possibility (i) to apply the method to even heavier systems than those (e.g., 74Ni) already studied so far and (ii) to perform converged Gorkov SCGF calculations based on harder, e.g. original chiral interactions.File  Dimensione  Formato  

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