Hierarchy of Self-Consistent Approximate Methods and the Parquet ...

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application II: Hubbard model (N c = 4 × 4) U = 2t, T = 0.3t S. X. Yang et al., PRE 80, 046706 (2009). Hierarchy of Self-Consistent Approximate Methods and the Parquet Formalism 38
Conclusion • Parquet formalism • Hierarchy of different approximate methods 1-particle 2-particle F = 0 F ≈ v Γ ≈ v Λ ≈ v re irre fully irre G T Σ S.D. χ F Γ Λ B.S. more localized Parquet H-F SOPT RPA, TMA, FLEX Parquet Approximation Λ II ≈ Λ I,DCA/QMC Better approximation DCA/QMC+Parquet MSMB Hierarchy of Self-Consistent Approximate Methods and the Parquet Formalism 39
Page 1 and 2: Hierarchy of Self-Consistent Approx
Page 3 and 4: Motivation For the strongly-correla
Page 5 and 6: Green function and self-energy (x 2
Page 7 and 8: Schwinger-Dyson equation Schwinger-
Page 9 and 10: Vertex v + initial 3 1 + + 4 H 2 P
Page 11 and 12: scattering channels p-h horizontal
Page 13 and 14: 1-particle reducibility reducible +
Page 21 and 22: Bethe-Salpeter equation and Parquet
Page 23 and 24: Hierarchy of self-consistent approx
Page 31 and 32: Parquet approximation: Λ ≈ v •
Page 33 and 34: DCA/QMC + parquet: Λ II ≈ Λ I,D
Page 35 and 36: application I: toy model The Hamilt
Page 37: application II: Hubbard model (N c

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