Test of the Bardeen-Cooper-Schrieffer and the resonant-valence-bond wave functions as solutions of the Hubbard model: A small-cluster calculation

Journal Article · Tue Jun 01 00:00:00 EDT 1993 · Physical Review, B: Condensed Matter; (United States)

DOI:https://doi.org/10.1103/PhysRevB.47.14407· OSTI ID:5528763

Falicov, L M; Proetto, C R ^[1]

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1. Centro Atomico Bariloche and Instituto Balseiro, Comision Nacional de Energia Atomica, 8400 S.C. de Bariloche, Rio Negro (Argentina)

With the purpose of assessing the validity of commonly used approximations, best variational solutions are calculated for a four-site (tetrahedral-cluster) Hubbard model with periodic boundary conditions and compared with exact results. In particular, the optimum number-conserving Bardeen-Cooper-Schrieffer-type variational solution is obtained for two, four, and six electrons, and the optimal resonanting-valence-bond state for four electrons. For an attractive interaction [ital U], the exact ground state of the system is obtained in all four cases. If the interaction [ital U] is repulsive, the exact ground state is obtained only when the cluster contains two and six electrons. For four electrons the BCS approximation is only satisfactory for relatively small [ital U]. For any positive [ital U] the resonating-valence-bond state on the other hand, gives very good (albeit not exact) energies for the ground state.

• OSTI ID: 5528763
• Journal Information: Physical Review, B: Condensed Matter; (United States), Vol. 47:21; ISSN 0163-1829
• Country of Publication: United States
• Language: English

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