### Abstract

The mixed valence trial ground state suggested by Stevens and Brandow is reconsidered in the case of two electrons per atom. The wellknown difficulties due to nonorthogonality are resolved by expanding the trial state in an orthonormal basis. The expansion coefficients are determinants composed of Bloch phase factors, as in the Gutzwiller method. Studying first the limiting case of the Kaplan-Mahanti strongly localized ground state in the Brandow formalism, we derive rules for a simplified handling of the determinants; this opens the way to the more complicated weakly localized ground state. This is handled by expressing the N variational parameters of the Brandow formalism through a single one, the "hybridization temperature" τ. The ground state energy is a well-behaved function of the hybridization matrix element V. The valence and the shift of the Fermi level are calculated to lowest order in V. The band occupation numbers follow a Fermi distribution at "temperature" τ∼V. We argue that the ground state is insulating, with the d-electrons localized into large Wannier-type orbitals centered on the respective f-holes, as envisaged by Stevens.

Original language | English |
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Pages (from-to) | 301-313 |

Number of pages | 13 |

Journal | Zeitschrift für Physik B Condensed Matter |

Volume | 47 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1982 |

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### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

**A single-parameter trial wave function for the mixed valence ground state.** / Fazekas, P.

Research output: Contribution to journal › Article

*Zeitschrift für Physik B Condensed Matter*, vol. 47, no. 4, pp. 301-313. https://doi.org/10.1007/BF01313796

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TY - JOUR

T1 - A single-parameter trial wave function for the mixed valence ground state

AU - Fazekas, P.

PY - 1982

Y1 - 1982

N2 - The mixed valence trial ground state suggested by Stevens and Brandow is reconsidered in the case of two electrons per atom. The wellknown difficulties due to nonorthogonality are resolved by expanding the trial state in an orthonormal basis. The expansion coefficients are determinants composed of Bloch phase factors, as in the Gutzwiller method. Studying first the limiting case of the Kaplan-Mahanti strongly localized ground state in the Brandow formalism, we derive rules for a simplified handling of the determinants; this opens the way to the more complicated weakly localized ground state. This is handled by expressing the N variational parameters of the Brandow formalism through a single one, the "hybridization temperature" τ. The ground state energy is a well-behaved function of the hybridization matrix element V. The valence and the shift of the Fermi level are calculated to lowest order in V. The band occupation numbers follow a Fermi distribution at "temperature" τ∼V. We argue that the ground state is insulating, with the d-electrons localized into large Wannier-type orbitals centered on the respective f-holes, as envisaged by Stevens.

AB - The mixed valence trial ground state suggested by Stevens and Brandow is reconsidered in the case of two electrons per atom. The wellknown difficulties due to nonorthogonality are resolved by expanding the trial state in an orthonormal basis. The expansion coefficients are determinants composed of Bloch phase factors, as in the Gutzwiller method. Studying first the limiting case of the Kaplan-Mahanti strongly localized ground state in the Brandow formalism, we derive rules for a simplified handling of the determinants; this opens the way to the more complicated weakly localized ground state. This is handled by expressing the N variational parameters of the Brandow formalism through a single one, the "hybridization temperature" τ. The ground state energy is a well-behaved function of the hybridization matrix element V. The valence and the shift of the Fermi level are calculated to lowest order in V. The band occupation numbers follow a Fermi distribution at "temperature" τ∼V. We argue that the ground state is insulating, with the d-electrons localized into large Wannier-type orbitals centered on the respective f-holes, as envisaged by Stevens.

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U2 - 10.1007/BF01313796

DO - 10.1007/BF01313796

M3 - Article

AN - SCOPUS:30244432484

VL - 47

SP - 301

EP - 313

JO - Zeitschrift für Physik B Condensed Matter and Quanta

JF - Zeitschrift für Physik B Condensed Matter and Quanta

SN - 1434-6028

IS - 4

ER -