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 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.

中文翻译：

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可积配对模型在​​双占配置交互空间中对变分降低密度矩阵理论进行基准测试

变分缩减密度矩阵理论最近已成功地应用于截短的双重占据构型交互空间内的模型，该空间对应于资历为零的子空间。资历量子数的守恒将哈密顿量限制为基于SU（2）代数。其中有一个完全可解决的Richardson-Gaudin配对哈密顿量的全族。我们将变分理论与两种不同的完全可解模型（Richardson-Gaudin-Kitaev和简化的BCS哈密顿量）进行基准比较。我们获得了所谓的N的精确数值结果-在两种情况下，对于10到100粒子的系统，都具有代表性。但是，当考虑适合于小的超导晶粒的随机单粒子能量时，虽然丧失了精度，但是仍然获得了很高的精度。