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
Tc 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
Tc dome against the effective electron-electron interaction
Ueff 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
Ueff=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.
The appearance of certain spectral features in one-dimensional (1D) cuprate materials has been attributed to a strong, extended attractive coupling between electrons. Here, using time-dependent density matrix renormalization group methods on a Hubbard-extended Holstein model, we show that extended electron-phonon ({\it e-ph}) coupling presents an obvious choice to produce such an attractive interaction that reproduces the observed spectral features and doping dependence seen in angle-resolved photoemission experiments: diminished
3kF spectral weight, prominent spectral intensity of a holon-folding branch, and the correct holon band width. While extended {\it e-ph} coupling does not qualitatively alter the ground state of the 1D system compared to the Hubbard model, it quantitatively enhances the long-range superconducting correlations and suppresses spin correlations. Such an extended {\it e-ph} interaction may be an important missing ingredient in describing the physics of the structurally similar two-dimensional high-temperature superconducting layered cuprates, which may tip the balance between intertwined orders in favor of uniform
d-wave superconductivity.
We investigate the interplay of electron–phonon (EP) coupling and strong electronic correlations in the frame of the two–dimensional (2D) Holstein t–J model (HtJM), focusing on polaronic ordering phenomena for the quarter–filled band case. The use of direct Lanczos diagonalization on finite lattices allows us to include the effects of quantum phonon fluctuations in the calculation of spin/charge structure factors and hole–phonon correlation functions. In the adiabatic strong coupling regime we found evidence for “self-localization ” of polaronic carriers in a (π, π) charge-modulated structure, a type of superlattice solidification reminiscent of those observed in the nickel perovskites La2−xSrxNiO4+y. Electron diffraction measurements on the nickel oxide analogue of the layered high–Tc 214 copper oxide compound, La2−xNixCuO4, reveal a (π, π)–superstructure spot at quarter filling, i.e. for x = 0.5, which has been interpreted as sign of a truly 2D polaron ordered phase [1]. To study charge – and spin–ordering phenomena in such systems, exhibiting besides a substantial EP interaction strong Coulomb correlations, let us consider the planar t-J model with an additional on-site Holstein hole-phonon coupling:
The density-matrix renormalization group is used to study the pairing when both electron-electron and electron-phonon interactions are strong in the Holstein-Hubbard model at half filling in a region intermediate between the adiabatic (Migdal's) and antiadiabatic limits. We have found (i) the pairing correlation obtained for a one-dimensional system is nearly degenerate with the charge density-wave correlation in a region where the phonon-induced attraction is comparable with the electron-electron repulsion, but (ii) pairing becomes dominant when we destroy the electron-hole symmetry in a trestle lattice. This provides an instance in which pairing can arise, in a lattice-structure dependent manner, from coexisting electron-electron and electron-phonon interactions.
In quantum materials, the electronic interaction and the electron-phonon coupling are in general two essential ingredients, the combined impact of which may drive exotic phases. Recently, an anomalously strong electron-electron attraction, mediated by phonons, has been unveiled in one-dimensional (1D) copper-oxide chain compound. Yet it is unclear how this strong near-neighbor (NN) attraction
V influences the superconductivity pairing. In this work, we employ the density-matrix renormalization group (DMRG) method to study this experiment-relevant extended Hubbard model with on-site Coulomb repulsion
U>0 and NN attraction
V<0, relevant for the 1D cuprate chain and likely other similar transition-metal materials. We find this extended
t-
U-
V model hosts a rich quantum phase diagram consisting of the spin density wave phase, phase separation phases, the Tomonaga-Luttinger liquid (TLL) phase, and especially an intriguing TLL regime with divergent superconducting susceptibility and dominant spin-triplet pair correlations. Upon doping, such a spin-triplet pairing regime can be further broadened in the parameter space and extends to larger
U. Our results show robust triplet pairing induced by attractive interaction
V, offering a feasible mechanism to realize
p-wave superconductivity in 1D cuprates.
The effects of the electron-phonon interaction on charge and spin dynamics are studied for the one-dimensional two-band Hubbard model by the exact diagonalization method. The parameters of the model are chosen to represent a hole-doped Cu-O system. Local charge fluctuations induced by phonons are expressed in terms of microscopic current and polarization, and it is shown that the dynamic charge transfer is strongly dependent on the phonon wave vector when the system is doped with holes. The dynamic magnetic structure factor is also found to be significantly modified by lattice distortion. In particular the lowest-energy spin excitations are greatly softened, indicating significant spin-phonon coupling. It is shown that the optical response is significantly modified as well due to coupling with the lattice over an energy range far exceeding the phonon energy. These results demonstrate the unconventional nature of the electron-phonon coupling in the strongly correlated electron systems. Its possible implications to the pairing mechanism in the cuprates are discussed.