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 ${U}_{\text{eff}}$ 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 $\ensuremath{\Delta}$ and $2\ensuremath{\Delta}/{T}_{c}$ 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 ${U}_{\mathrm{eff}}=0$ , while the two phases are separated by a paramagnetic metal in the weak-coupling regime and a paramagnetic insulator in the strong-coupling regime.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 ${U}_{\text{eff}}$ 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 $\ensuremath{\Delta}$ and $2\ensuremath{\Delta}/{T}_{c}$ 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 ${U}_{\mathrm{eff}}=0$, while the two phases are separated by a paramagnetic metal in the weak-coupling regime and a paramagnetic insulator in the strong-coupling regime.

arXiv:1305.5771Physical Review BSep 16, 201362 citations

Continuous-Time Quantum Monte Carlo Study of Strong Coupling Superconductivity in Holstein–Hubbard Model

Satoshi Yamazaki, Shintaro Hoshino, Yoshio Kuramoto

Superconducting transition temperature is studied in the strong-coupling region of the Holstein-Hubbard model that includes both electron-phonon and Coulomb interactions.By combining the dynamical mean field theory with the continuous-time quantum Monte Carlo method, transition temperature is derived numerically.Without Coulomb interaction, our calculation reproduces analytic expressions of the transition temperature for weak and strong coupling limits of electron-phonon interaction.When electron-phonon coupling is strong enough, Coulomb repulsion enhances superconductivity, in contrast to the weak coupling case.The enhancement is due to coherent motion of superconducting pairs that reduce the Coulomb repulsive energy of almost localized electrons.Superconducting transition temperature is studied in the strong-coupling region of the Holstein-Hubbard model that includes both electron-phonon and Coulomb interactions.By combining the dynamical mean field theory with the continuous-time quantum Monte Carlo method, transition temperature is derived numerically.Without Coulomb interaction, our calculation reproduces analytic expressions of the transition temperature for weak and strong coupling limits of electron-phonon interaction.When electron-phonon coupling is strong enough, Coulomb repulsion enhances superconductivity, in contrast to the weak coupling case.The enhancement is due to coherent motion of superconducting pairs that reduce the Coulomb repulsive energy of almost localized electrons.

International Conference on Strongly Correlated Electron Systems (SCES)Jun 16, 20142 citations

Electron-phonon superconductivity mechanisms in the Hubbard model

Chan Minh Tien

Theoretical and Mathematical PhysicsJun 1, 19920 citations

Strong coupling Hubbard model and superconductivity

M. Noga

Czechoslovak Journal of PhysicsNov 1, 19890 citations

Synergistic Polaron Formation in the Hubbard-Holstein Model at Small Doping

Alexandru Macridin, Brian Moritz, M. Jarrell +1 more

We study the effect of dynamical Holstein phonons on the physics of the Hubbard model at small doping using the dynamical cluster approximation on a 2x2 cluster. Nonlocal antiferromagnetic correlations are found to significantly enhance the electron-phonon coupling, resulting in polaron formation for moderate coupling strengths. At finite doping, the electron-phonon coupling is found to strongly enhance the nonlocal spin correlations, indicating a synergistic interplay between the electron-phonon coupling and antiferromagnetic correlations. Although it enhances the pairing interaction, the electron-phonon coupling is found to decrease the superconducting transition temperature, due to the reduction in the quasiparticle fraction.We study the effect of dynamical Holstein phonons on the physics of the Hubbard model at small doping using the dynamical cluster approximation on a 2x2 cluster. Nonlocal antiferromagnetic correlations are found to significantly enhance the electron-phonon coupling, resulting in polaron formation for moderate coupling strengths. At finite doping, the electron-phonon coupling is found to strongly enhance the nonlocal spin correlations, indicating a synergistic interplay between the electron-phonon coupling and antiferromagnetic correlations. Although it enhances the pairing interaction, the electron-phonon coupling is found to decrease the superconducting transition temperature, due to the reduction in the quasiparticle fraction.

arXiv:cond-mat/0607623Physical Review LettersAug 2, 200649 citations

{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}_{\text{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 $\ensuremath{\Delta}$ and $2\ensuremath{\Delta}/{T}_{c}$ 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}_{\mathrm{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.