Reduced density matrices of Richardson-Gaudin states in the Gaudin\n algebra basis

2020/08/28 by Charles‐Émile Fecteau, Fecteau, Charles-Émile, Hubert Fortin +5 · 2 citations
Chemistry · Physics and Astronomy · #Advanced Chemical Physics Studies #Chemical Physics (physics.chem-ph) #FOS: Physical sciences #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality #Spectroscopy and Quantum Chemical Studies

paper · pdf · doi:10.48550/arxiv.2008.12713

openalex publication_date 2020/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Eigenvectors of the reduced Bardeen-Cooper-Schrieffer Hamiltonian have\nrecently been employed as a variational wavefunction ansatz in quantum\nchemistry. This wavefunction is a mean-field of pairs of electrons (geminals).\nIn this contribution we report optimal expressions for their reduced density\nmatrices in both the original physical basis and the basis of the\nRichardson-Gaudin pairs. Physical basis expressions were originally reported by\nGorohovsky and Bettelheim. In each case, the expressions scale like\n\O(N⁴), with the most expensive step the solution of linear\nequations. Analytic gradients are also reported in the physical basis. These\nexpressions are an important step towards practical mean-field methods to treat\nstrongly-correlated electrons.\n

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