Ordered phases in the Holstein-Hubbard model: Interplay of strong Coulomb interaction and electron-phonon coupling

Murakami, Yuta; Werner, Philipp; Tsuji, Naoto; Aoki, Hideo

doi:10.1103/PhysRevB.88.125126

Back

Journal article

Ordered phases in the Holstein-Hubbard model: Interplay of strong Coulomb interaction and electron-phonon coupling

Murakami, Yuta Department of Physics, University of Tokyo, Japan
Werner, Philipp Department of Physics, University of Fribourg, Switzerland
Tsuji, Naoto Department of Physics, University of Tokyo, Japan
Aoki, Hideo Department of Physics, University of Tokyo, Japan

16.09.2013

Published in:

Physical Review B. - 2013, vol. 88, no. 12, p. 125126

English 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 T_c 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 T_c dome against the effective electron-electron interaction U_eff given by the Hubbard U 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 Δ and 2Δ/T_c 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 U_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.

Faculty

Faculté des sciences et de médecine

Department

Département de Physique

Language