Abstract
For many-electron systems, the second-order reduced density matrix (2-RDM) provides sufficient information for characterizing their properties of interests in physics and chemistry. In this paper, we present a set of nontrivial constraints on 2-RDM based on the basic geometric property of Hilbert space and the commutation relations of operators. Numerical examples are provided to demonstrate the pronounced violation of these constraints by the variational 2-RDMs. It is shown that, for a strongly correlated model system, the constraint violation may be responsible for a considerable portion of the variational error in ground-state energy. Our findings provide new insights into the structural subtlety of many-electron 2-RDMs.
- Received 23 November 2020
- Revised 18 April 2021
- Accepted 19 April 2021
DOI:https://doi.org/10.1103/PhysRevA.103.052202
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