Combining symmetry breaking and restoration with configuration interaction: A highly accurate many-body scheme applied to the pairing Hamiltonian
Combining symmetry breaking and restoration with configuration interaction: A highly accurate many-body scheme applied to the pairing Hamiltonian
复制标题
将对称性破缺和恢复与构型相互作用相结合：应用于配对哈密顿量的高精度多体方案
DOI：
10.1103/physrevc.95.014326
复制
发表时间：
2016
影响因子：
3.1
通讯作者：
T. Duguet
中科院分区：
文献类型：
--
作者：
J. Ripoche;D. Lacroix;D. Gambacurta;J. Ebran;T. Duguet
背景：在过去的十年里，从头算多体方法已经发展到解决中等质量核...随着核子间相互作用的设计取得进展，必须进一步努力使多体方法适应。研究方法：我们制定了一个截断组态相互作用的方法，包括对角化的哈密顿量在一个高度截断的子空间的总N体希尔伯特空间。约化希尔伯特空间是由粒子数投影BCS态沿着与投影优先级零、二和四准粒子激发产生的。此外，在投影的两个和四个准粒子激发的存在下，基本BCS态破坏U（1）对称性的程度得到了优化。新设计的方法的质量进行测试对所谓的吸引配对哈密顿问题的精确解。结果：通过构建，该方法重现了N=2和N=4的精确结果。当N=（8，16，20）时，在整个核子间耦合范围内，基态关联能的误差小于（0.006，0.1，0.15）%.目前提出的方法提供了自动访问低位光谱的优点，其具有高精度。结论：新设计的变分方法的数值代价是多项式（N$^6$）的系统规模。它实现了一个前所未有的准确的基态关联能，有效的配对间隙和单体熵，以及对吸引配对哈密顿量的低位态的激发能。这构成了一个足够强大的动机，设想其应用到现实的核哈密顿考虑提供一个互补的，准确的和通用的从头计算描述中质量开壳层原子核在未来。
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.