零简态线性规范变换理论
Seniority-zero Linear Canonical Transformation Theory
AI总结：
本文提出了一种通过单位变换降低强关联系统电子薛定谔方程复杂度的方法，利用零简态空间简化计算并保留电子对间强关联，采用BCH展开和规范变换理论中的算子分解策略，实现高精度计算，计算复杂度为O(N^8/n_c)。
摘要：
我们提出了一种通过对物理哈密顿量施加幺正变换来求解强关联系统电子薛定谔方程的方法。特别地，我们寻找一种变换，将哈密顿量映射到零简态空间：零简态波函数计算更简单，但仍能捕捉电子对间的强关联。幺正旋转通过 Baker-Campbell-Hausdorff (BCH) 展开评估，截断至两体算符通过规范变换理论中的算子分解策略，将高阶项近似表示为一、两体算符。与传统规范变换理论方法不同，生成器被选择以最小化变换后哈密顿量中非零简态部分的大小。数值测试表明，这种零简态线性规范变换 (SZ-LCT) 方法能提供高精度结果，通常误差小于毫赫特。SZ-LCT 的有效计算复杂度为 $\mathcal{O}(N^8/n_c)$，其中 $n_c$ 是可用于计算的核心数。
英文摘要：
We propose a method to solve the electronic Schrödinger equation for strongly correlated systems by applying a unitary transformation to reduce the complexity of the physical Hamiltonian. In particular, we seek a transformation that maps the Hamiltonian into the seniority-zero space: seniority-zero wavefunctions are computationally simpler, but still capture strong correlation within electron pairs. The unitary rotation is evaluated using the Baker Campbell Hausdorff (BCH) expansion, truncated to two-body operators through the operator decomposition strategy of canonical transformation (CT) theory, which rewrites higher-rank terms approximately in terms of one- and two-body operators. Unlike conventional approaches to CT theory, the generator is chosen to minimize the size of non-seniority-zero elements of the transformed Hamiltonian. Numerical tests reveal that this Seniority-zero Linear Canonical Transformation (SZ-LCT) method delivers highly accurate results, usually with submilliHartree error. The effective computational scaling of SZ-LCT is $\mathcal{O}(N^8/n_c)$ , where $n_c$ is the number of cores available for the computation.
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