Representability for Quantum Theory beyond Particle-Number Conservation

• URL: http://arxiv.org/abs/2604.23869v1
• Date: Sun, 26 Apr 2026 20:21:06 GMT
• Title: Representability for Quantum Theory beyond Particle-Number Conservation
• Abstract summary: Representability determines when a two-particle reduced density matrix (2-RDM) corresponds to a physical quantum state.<n>We present a solution of the representability problem for quantum systems without particle-number conservation.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Representability determines when a two-particle reduced density matrix (2-RDM) corresponds to a physical quantum state, enabling many-particle quantum calculations with 2-RDMs rather than the wave function. In this Letter, we present a solution of the representability problem for quantum systems without particle-number conservation. The physically allowed set of 2-RDMs can be characterized from a geometrically `orthogonal' set, the polar cone. We derive explicit linear equations for the two-body operators in the polar cone -- the intersection of the $p$-positive cone with the two-body operator space -- to obtain a systematic hierarchy of representability conditions that do not depend on higher RDMs or the wave function. Moreover, by augmenting these conditions with the particle-number variance, we obtain a unified framework for treating both particle-number-conserving and nonconserving systems. We illustrate with a spin system and molecular H$_4$.

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