su(2)哈密顿量的Bogoliubov耦合簇理论

中文摘要 AI 辅助

耦合簇理论是弱关联系统的首选方法，但在平均场参考态质量较差的强关联系统中，它可能严重失效。这些失败可以通过使用对称性破缺的平均场参考态来改善。对于自发破缺自旋对称性的系统，我们可能倾向于使用非限制性参考态。在破缺粒子数对称性的系统中，我们转而采用Bogoliubov耦合簇理论。在本工作中，我们将Bogoliubov耦合簇应用于具有底层su(2)代数的哈密顿量，利用费米子对算符与自旋-1/2算符之间的对应关系，研究配对哈密顿量以及自旋XXZ和J1-J2模型。对于配对问题，参考态是通常的Bardeen-Cooper-Schrieffer（BCS）准粒子真空，而对于自旋系统，我们使用类似的spin-BCS参考态，它破缺Sz对称性，并为强关联区域提供了灵活的起点。关联通过一系列耦合簇近似纳入。除能量外，我们还计算响应密度矩阵以评估XXZ和J1-J2海森堡模型的自旋-自旋关联函数，以及配对哈密顿量的配对参数和粒子数方差。我们还推导了相应的弛豫密度矩阵，包括轨道弛豫效应。半填充配对哈密顿量和自旋模型的基准计算表明，Bogoliubov耦合簇为su(2)哈密顿量提供了一种可系统改进的基于波函数的方法，包括需要复数和非共线BCS参考态的几何阻挫自旋系统。

英文摘要

Coupled-cluster theory is the method of choice for weakly correlated systems, but in strongly correlated systems where the mean-field reference is qualitatively poor, it can break down badly. These failures can be ameliorated by using symmetry-broken mean-field references. For systems that spontaneously break spin symmetry, we might favor an unrestricted reference. In systems that instead break number symmetry, we turn to Bogoliubov coupled cluster theory. In this work, we apply Bogoliubov coupled-cluster to Hamiltonians with an underlying su(2) algebra to study the pairing Hamiltonian and the spin XXZ and J1-J2 models by exploiting the correspondence between fermionic-pair operators and spin-1/2 operators. For the pairing problem, the reference is the usual Bardeen--Cooper--Schrieffer (BCS) quasiparticle vacuum, while for spin systems we use the analogous spin-BCS reference, which breaks Sz symmetry and provides a flexible starting point for strongly correlated regimes. Correlation is incorporated through a hierarchy of coupled-cluster approximations. Beyond energies, we compute the response density matrices for the evaluation of spin--spin correlation functions for the XXZ and J1-J2 Heisenberg models, and the pairing parameter and particle-number variance for the pairing Hamiltonian. We also derive the corresponding relaxed density matrices, including the effects of orbital relaxation. Benchmark calculations for the half-filled pairing Hamiltonian and spin models demonstrate that Bogoliubov coupled cluster provides a systematically improvable wave-function-based approach for su(2) Hamiltonians, including geometrically frustrated spin systems requiring complex and noncollinear BCS references.

发表机构

• Rice University（莱斯大学）

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