Spin adaptation of the cumulant expansions of reduced density matrices

2025/05/22 by Liebert, Julia, Schilling, Christian, Mazziotti, David A.
#Chemical Physics (physics.chem-ph) #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2505.16989

Abstract

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 S² 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 S², 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.

Citations

• Projective purification of correlated reduced density matrices
• Advancing Natural Orbital Functional Calculations Through Deep Learning-Inspired Techniques for Large-Scale Strongly Correlated Electron Systems
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• The fractional quantum Hall effect
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