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Self-Consistent Fluctuation Theory for Strongly Correlated Electron Systems

A self-consistent theory for two-particle fluctuations with renormalized irreducible vertices is proposed. Using the Parquet formalism, we construct the fully antisymmetric full vertex in terms of the two-particle fluctuations in the charge, the spin and the particle-particle channels on an equal footing to satisfy the Pauli principle. The fluctuations are determined self-consistently, which are reflected into the one-particle self-energy via the Schwinger-Dyson equation. We demonstrate the application of the present theory to the impurity Anderson model and the Hubbard model on a square lattice mainly for the particle-hole symmetric case. In both models the vertex renormalization in the spin channel eliminates magnetic instabilities of mean-field theory to ensure the Mermin-Wagner theorem. The present theory gives the same critical exponents of the self-consistent renormalization theory in the quantum critical region.