Quantum Many-body Theory from a Solution of the $N$-representability Problem

• URL: http://arxiv.org/abs/2304.08570v1
• Date: Mon, 17 Apr 2023 19:19:31 GMT
• Title: Quantum Many-body Theory from a Solution of the $N$-representability Problem
• Authors: David A. Mazziotti
• Abstract summary: We derive an equation that re-expresses physical constraints on higher-order RDMs to generate direct constraints on the 2-RDM. We illustrate by computing the ground-state electronic energy and properties of the H$_8$ ring.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Here we present a many-body theory based on a solution of the $N$-representability problem in which the ground-state two-particle reduced density matrix (2-RDM) is determined directly without the many-particle wave function. We derive an equation that re-expresses physical constraints on higher-order RDMs to generate direct constraints on the 2-RDM, which are required for its derivation from an $N$-particle density matrix, known as $N$-representability conditions. The approach produces a complete hierarchy of 2-RDM constraints that do not depend explicitly upon the higher RDMs or the wave function. By using the two-particle part of a unitary decomposition of higher-order constraint matrices, we can solve the energy minimization by semidefinite programming in a form where the low-rank structure of these matrices can be potentially exploited. We illustrate by computing the ground-state electronic energy and properties of the H$_{8}$ ring.

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