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An investigation is presented of the utility of semiclassical approximationsfor solving the quantum-impurity problems arising in the dynamical-mean-fieldapproach to the correlated-electron models. The method is based on performing aexact numerical integral over the zero-Matsubara-frequency component of thespin part of a continuous Hubbard-Stratonovich field, along with aspin-field-dependent steepest descents treatment of the charge part. We testthis method by applying it to one or two site approximations to the single bandHubbard model with different band structures, and comparing the results toquantum Monte-Carlo and simplified exact diagonalization calculations. Theresulting electron self-energies, densities of states and magnetic transitiontemperatures show reasonable agreement with the quantum Monte-Carlo simulationover wide parameter ranges, suggesting that the semiclassical method is usefulfor obtaining a reasonable picture of the physics in situations where othertechniques are too expensive.Comment: 14 pages, 15 figure

physical review. b, condensed matter and materials physics

Benchmarkings for a semiclassical impurity solver for dynamical-mean-field theory: Self-energies and magnetic transitions of the single-orbital Hubbard model