Particle-number projected Bogoliubov-coupled-cluster theory: Application to the pairing Hamiltonian
Particle-number projected Bogoliubov-coupled-cluster theory: Application to the pairing Hamiltonian
复制标题
DOI：
10.1103/physrevc.99.044301
复制
发表时间：
2018-10
影响因子：
3.1
通讯作者：
Y. Qiu;T. M. Henderson;T. Duguet;T. Duguet;G. Scuseria
中科院分区：
文献类型：
--
作者：
Y. Qiu;T. M. Henderson;T. Duguet;T. Duguet;G. Scuseria
背景：虽然耦合簇理论准确地模拟了弱相关量子系统，但在强相关性存在的情况下，它通常会失败，而标准平均场图像在质量上是不正确的。在许多情况下，通过允许平均场参考打破物理对称性可以很大程度上改善这些故障。对称破缺耦合团簇，例如博戈柳波夫耦合团簇，理论确实可以提供相当准确的能量预测，但破缺对称性可能会损害所得波函数的质量以及除能量之外的可观测量的预测。目的：因此，将对称投影和耦合簇理论相结合是描述强相关系统的一种有吸引力的方法。人们确实期望继承并进一步提高破缺对称耦合簇的能量精度，同时保留适当的对称性。方法：最近独立地提出了两种不同但相关的形式主义来实现这一目标。本手稿对这两种形式进行了对比，并在理查森配对哈密顿量上测试了结果。虽然本文重点关注与粒子数守恒相关的 U(1) 全局规范对称性的破坏和恢复，但对称投影耦合簇形式主义也适用于其他对称性，例如旋转（即自旋）对称性。结果：两种形式都是基于对称旋转耦合簇波函数的解纠缠簇表示。然而，它们在解纠缠簇的解决方式上有所不同。一种方法建立与角度相关的耦合簇方程，而另一种方法涉及一阶常微分方程。后一种方法产生的能量和占据概率明显优于数投影 Bardeen-Cooper-Schrieffer (BCS) 和 BCS 耦合簇，并且当在低激励水平下截断解纠缠簇时，其计算成本不会比 BCS 耦合簇大太多。结论：本手稿中提出的高质量结果表明，对称投影耦合簇是一种有前途的方法，可以准确描述弱相关和强相关的有限多费米子系统。
Background: While coupled-cluster theory accurately models weakly correlated quantum systems, it often fails in the presence of strong correlations where the standard mean-field picture is qualitatively incorrect. In many cases, these failures can be largely ameliorated by permitting the mean-field reference to break physical symmetries. Symmetry-broken coupled-cluster, e.g., Bogoliubov-coupled-cluster, theory can indeed provide reasonably accurate energetic predictions, but the broken symmetry can compromise the quality of the resulting wave function and predictions of observables other than the energy. Purpose: Merging symmetry projection and coupled-cluster theory is therefore an appealing way to describe strongly correlated systems. One indeed expects to inherit and further improve the energetic accuracy of broken-symmetry coupled cluster while retaining proper symmetries. Methods: Independently, two different but related formalisms have been recently proposed to achieve this goal. The two formalisms are contrasted in this manuscript, with results tested on the Richardson pairing Hamiltonian. While the present paper focuses on the breaking and restoration of U(1) global-gauge symmetry associated with particle-number conservation, the symmetry-projected coupled-cluster formalism is applicable to other symmetries such as rotational (i.e., spin) symmetry. Results: Both formalisms are based on the disentangled cluster representation of the symmetry-rotated coupled-cluster wave function. However, they differ in the way that the disentangled clusters are solved. One approach sets up angle-dependent coupled-cluster equations, while the other involves first-order ordinary differential equations. The latter approach yields energies and occupation probabilities significantly better than those of number-projected Bardeen-Cooper-Schrieffer (BCS) and BCS coupled cluster and, when the disentangled clusters are truncated at low excitation levels, has a computational cost not too much larger than that of BCS coupled cluster. Conclusions: The high quality of results presented in this manuscript indicates that symmetry-projected coupled cluster is a promising method that can accurately describe both weakly and strongly correlated finite many-fermion systems.