{'fraction_non_alphanumeric': 0.014308426073131956, 'fraction_numerical': 0.0, 'mean_word_length': 5.456410256410257, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Dynamical Cluster Approximation Employing FLEX as a Cluster Solver

We employ the Dynamical Cluster Approximation (DCA) in conjunction with the Fluctuation Exchange Approximation (FLEX) to study the Hubbard model. The DCA is a technique to systematically restore the momentum conservation at the internal vertices of Feynman diagrams relinquished in the Dynamical Mean Field Approximation (DMFA). FLEX is a perturbative diagrammatic approach in which classes of Feynman diagrams are summed over analytically using geometric series. The FLEX is used as a tool to investigate the complementarity of the DCA and the finite size lattice technique with periodic boundary conditions by comparing their results for the Hubbard model. We also study the microscopic theory underlying the DCA in terms of compact (skeletal) and noncompact diagrammatic contributions to the thermodynamic potential independent of a specific model. The significant advantages of the DCA implementation in momentum space suggests the development of the same formalism for the frequency space. However, we show that such a formalism for the Matsubara frequencies at finite temperatures leads to acausal results and is not viable. However, a real frequency approach is shown to be feasible.