Combining symmetry breaking and restoration with configuration interaction: a highly accurate many-body scheme applied to the pairing Hamiltonian

TL;DR

This paper introduces a highly accurate truncated configuration interaction method that combines symmetry breaking and restoration, optimized for the pairing Hamiltonian, achieving near-exact results with polynomial computational cost.

Contribution

The paper presents a novel variational method integrating symmetry projection with configuration interaction, significantly improving accuracy for the pairing Hamiltonian.

Findings

Reproduces exact results for small systems (N=2,4).

Achieves less than 0.15% error in ground-state energy for larger systems (N=8,16,20).

Provides high-accuracy low-lying spectroscopy and excitation energies.

Abstract

Background: Ab initio many-body methods have been developed over the past ten years to address mid-mass nuclei... As progress in the design of inter-nucleon interactions is made, further efforts must be made to tailor many-body methods. Methods: We formulate a truncated configuration interaction method that consists of diagonalizing the Hamiltonian in a highly truncated subspace of the total N-body Hilbert space. The reduced Hilbert space is generated via the particle-number projected BCS state along with projected seniority-zero two and four quasi-particle excitations. Furthermore, the extent by which the underlying BCS state breaks U(1) symmetry is optimized in presence of the projected two and four quasi-particle excitations... The quality of the newly designed method is tested against exact solutions of the so-called attractive pairing Hamiltonian problem. Results: By construction, the method reproduce exact results for N=2 and N=4. For N=(8,16,20) the error on the ground-state correlation energy is less than (0.006, 0.1, 0.15) % across the entire range of inter-nucleon coupling defining the pairing Hamiltonian and driving the normal-to-superfluid quantum phase transition. The presently proposed method offers the advantage to automatically access the low-lying spectroscopy, which it does with high accuracy. Conclusions: The numerical cost of the newly designed variational method is polynomial (N$^6$) in system size. It achieves an unprecedented accuracy on the ground-state correlation energy, effective pairing gap and one-body entropy as well as on the excitation energy of low-lying states of the attractive pairing Hamiltonian. This constitutes a strong enough motivation to envision its application to realistic nuclear Hamiltonians in view of providing a complementary, accurate and versatile ab initio description of mid-mass open-shell nuclei in the future.