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Dynamical vertex approximation is a Feynman diagrammatic extension of dynamical mean field theory, including non-local correlations on all time and length scales.
Methods of Quantum Field Theory in Statistical Physics
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For details on the numerical solution of the parquet equation and how to stabilize it enforcing among others the crossing symmetry, see S. X. Yang, H. Fotso, J. Liu, T. A. Maier, K. Tomko, E. F. D’Azevedo, R. T. Scalettar, T. Pruschke, and M. Jarrell, Phys. Rev. E 80, 046706 (2009); K.-M. Tam, H. Fotso, S.-X. Yang, Tae-Woo Lee, J. Moreno, J. Ramanujam, and M. Jarrell, Phys. Rev. E. 87
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