Instituto de Estructura de la Materia, CSIC, Serrano 123 , 28006 Madrid , Spain.
Departamento de Física, Facultad de Ciencias Exactas y Naturales , Universidad de Buenos Aires, Ciudad Universitaria , 1428 Buenos Aires , Argentina.
J Chem Theory Comput. 2018 Aug 14;14(8):4183-4192. doi: 10.1021/acs.jctc.8b00387. Epub 2018 Jul 9.
The variational reduced density matrix theory has been recently applied with great success to models within the truncated doubly occupied configuration interaction space, which corresponds to the seniority zero subspace. Conservation of the seniority quantum number restricts the Hamiltonians to be based on the SU(2) algebra. Among them there is a whole family of exactly solvable Richardson-Gaudin pairing Hamiltonians. We benchmark the variational theory against two different exactly solvable models, the Richardson-Gaudin-Kitaev and the reduced BCS Hamiltonians. We obtain exact numerical results for the so-called [Formula: see text] N-representability conditions in both cases for systems that go from 10 to 100 particles. However, when random single-particle energies as appropriate for small superconducting grains are considered, the exactness is lost but still a high accuracy is obtained.
变分约化密度矩阵理论最近已成功应用于截断的双占据组态相互作用空间内的模型，该空间对应于宇称零子空间。宇称量子数的守恒限制了哈密顿量基于 SU(2)代数。其中存在一整族完全可解的 Richardson-Gaudin 配对哈密顿量。我们将变分理论与两个不同的完全可解模型，Richardson-Gaudin-Kitaev 和约化 BCS 哈密顿量进行了基准测试。我们获得了两种情况下所谓的 [公式：见正文] N 表示条件的精确数值结果，系统从 10 到 100 个粒子。然而，当考虑适合小超导颗粒的随机单粒子能量时，精确性会丢失，但仍能获得高精度。
