Spin adaptation of the cumulant expansions of reduced density matrices
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912677606981632 |
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| author | Liebert, Julia Schilling, Christian Mazziotti, David A. |
| author_facet | Liebert, Julia Schilling, Christian Mazziotti, David A. |
| contents | We develop a systematic framework for the spin adaptation of the cumulants of p-particle reduced density matrices (RDMs), with explicit constructions for p = 1 to 3. These spin-adapted cumulants enable rigorous treatment of both S_z and S^2 symmetries in quantum systems, providing a foundation for spin-resolved electronic structure methods. We show that complete spin adaptation -- referred to as complete S-representability -- can be enforced by constraining the variances of S_z and S^2, which require the 2-RDM and 4-RDM, respectively. Importantly, the cumulants of RDMs scale linearly with system size -- size-extensive -- making them a natural object for incorporating spin symmetries in scalable electronic structure theories. The developed formalism is applicable to density-based methods (DFT), one-particle RDM functional theories (RDMFT), and two-particle RDM methods. We further extend the approach to spin-orbit-coupled systems via total angular momentum adaptation. Beyond spin, the framework enables the adaptation of RDM theories to additional symmetries through the construction of suitable irreducible tensor operators. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_16989 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spin adaptation of the cumulant expansions of reduced density matrices Liebert, Julia Schilling, Christian Mazziotti, David A. Chemical Physics Computational Physics Quantum Physics We develop a systematic framework for the spin adaptation of the cumulants of p-particle reduced density matrices (RDMs), with explicit constructions for p = 1 to 3. These spin-adapted cumulants enable rigorous treatment of both S_z and S^2 symmetries in quantum systems, providing a foundation for spin-resolved electronic structure methods. We show that complete spin adaptation -- referred to as complete S-representability -- can be enforced by constraining the variances of S_z and S^2, which require the 2-RDM and 4-RDM, respectively. Importantly, the cumulants of RDMs scale linearly with system size -- size-extensive -- making them a natural object for incorporating spin symmetries in scalable electronic structure theories. The developed formalism is applicable to density-based methods (DFT), one-particle RDM functional theories (RDMFT), and two-particle RDM methods. We further extend the approach to spin-orbit-coupled systems via total angular momentum adaptation. Beyond spin, the framework enables the adaptation of RDM theories to additional symmetries through the construction of suitable irreducible tensor operators. |
| title | Spin adaptation of the cumulant expansions of reduced density matrices |
| topic | Chemical Physics Computational Physics Quantum Physics |
| url | https://arxiv.org/abs/2505.16989 |