Murakami, Yuta Werner, Philipp Tsuji, Naoto Aoki, Hideo 2013-09-16 We study the Holstein-Hubbard model at half filling to explore ordered phases including superconductivity (SC), antiferromagnetism (AF), and charge order (CO) in situations where the electron-electron and electron-phonon interactions are strong (comparable to the electronic bandwidth). The model is solved in the dynamical mean-field approximation with a continuous-time quantum Monte Carlo impurity solver. We determine the superconducting transition temperature <i>T</i>_<i>c</i> and the SC order parameter and show that the phonon-induced retardation or the strong Coulomb interaction leads to a significant reduction and shift of the <i>T</i>_<i>c</i> dome against the effective electron-electron interaction <i>U</i>_eff given by the Hubbard <i>U</i> reduced by the phonon-mediated attraction in the static limit. This behavior is analyzed by comparison to an effective static model in the polaron representation with a renormalized bandwidth. In addition, we discuss the superconducting gap <i>Δ</i> and 2<i>Δ</i>/<i>T</i>_<i>c</i> to reveal the effect of the retardation and the Coulomb interaction. We also determine the finite-temperature phase diagram including AF and CO. In the moderate-coupling regime, there is a hysteretic region of AF and CO around <i>U</i>_eff=0, while the two phases are separated by a paramagnetic metal in the weak-coupling regime and a paramagnetic insulator in the strong-coupling regime. application/pdf https://folia.unifr.ch/global/documents/303350 https://folia.unifr.ch/documents/303350/files/wer_opf.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevB.88.125126 info:eu-repo/semantics/openAccess License undefined Physical Review B. - 2013, vol. 88, no. 12, p. 125126 info:eu-repo/classification/udc/53 Ordered phases in the Holstein-Hubbard model: Interplay of strong Coulomb interaction and electron-phonon coupling http://purl.org/coar/resource_type/c_6501