We study the Holstein-Hubbard model at half filling to explore the ordered phases such as the charge density wave and antiferromagnet. The Coulomb interaction is rewritten in terms of auxiliary fields. By treating the auxiliary fields and phonons as classical, we obtain real-space features of the system and transition between the phases from weak to strong coupling. When both interactions are weak, mutual competition between them leads to a metallic phase in an otherwise insulator-dominated phase diagram. Spatial correlations induced by thermal fluctuations lead to pseudogap features at intermediate range of coupling.
We study the Holstein-Hubbard model at half filling to explore the ordered phases such as the charge density wave and antiferromagnet. The Coulomb interaction is rewritten in terms of auxiliary fields. By treating the auxiliary fields and phonons as classical, we obtain real-space features of the system and transition between the phases from weak to strong coupling. When both interactions are weak, mutual competition between them leads to a metallic phase in an otherwise insulator-dominated phase diagram. Spatial correlations induced by thermal fluctuations lead to pseudogap features at intermediate range of coupling.
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 Hubbard-Holstein model is one of the simplest to incorporate both electron-electron and electron-phonon interactions. In one dimension at half filling, the Holstein electron-phonon coupling promotes on-site pairs of electrons and a Peierls charge-density wave, while the Hubbard on-site Coulomb repulsion U promotes antiferromagnetic correlations and a Mott insulating state. Recent numerical studies have found a possible third intermediate phase between Peierls and Mott states. From direct calculations of charge and spin susceptibilities, we show that (i) as the electron-phonon coupling is increased, first a spin gap opens, followed by the Peierls transition. Between these two transitions, the metallic intermediate phase has a spin gap, no charge gap, and properties similar to the negative-U Hubbard model. (ii) The transitions between Mott/intermediate and intermediate/Peierls states are of the Kosterlitz-Thouless form. (iii) For larger U, the two transitions merge at a tricritical point into a single first-order Mott/Peierls transition. In addition, we show that an intermediate phase also occurs in the quarter-filled model.
We present a numerical study of the Hubbard-Holstein model in one dimension at half filling, including finite-frequency quantum phonons. At half filling, the effects of the electron-phonon and electron-electron interactions compete with the Holstein phonon coupling acting as an effective negative Hubbard on-site interaction U that promotes on-site electron pairs and a Peierls charge-density wave state. Most previous work on this model has assumed that only Peierls or Mott phases are possible at half filling. However, there has been speculation that a third metallic phase exists between the Peierls and Mott phases. We confirm the intermediate phase, and show that the Luttinger liquid correlation exponent K(rho) >1 in this region, indicating dominant superconducting pair correlations. We explore the full phase diagram as a function of Hubbard U, phonon coupling constant, and phonon frequency.
We investigate the magnetotransport properties of the one-band Hubbard-Holstein model at half-filling in three dimensions (3D) using exact diagonalization based semi-classical Monte Carlo simulations with phonons treated in the adiabatic limit. The low-temperature electronic correlation U vs electron-phonon coupling V phase diagram reveals two insulating phases--antiferromagnetic (AF-I) and charge-ordered (CO-I)--separated by a first-order transition, with no metallic phase observed at their intersection, indicating robustness of these phases in 3D. For U∼bandwidth, the V vs temperature T phase diagram exhibits multiple phases including AF-I, CO-I, Mott-Hubbard insulator, bipolaronic insulator, and two bipolaronic metallic states. Several first-order transitions occur near V∼3.75. Above the ordering temperature, the density of states shows universal behavior dominated by electronic contribution, while susceptibility and DOS analyses reveal pseudogap features. Magnetic and transport properties along the phase boundary highlight strong proximity effects between competing phases, suggesting routes for tuning correlated materials and emergent electronic states.
Phase diagram of the two-dimensional Hubbard-Holstein model: enhancement of s-wave pairing between charge and magnetic orders
We investigate the role of electron-electron and electron-phonon interactions in strongly correlated systems by performing unbiased quantum Monte Carlo simulations in the square lattice Hubbard-Holstein model at half-filling. We study the competition and interplay between antiferromagnetism (AFM) and charge-density wave (CDW), establishing its very rich phase diagram. In the region between AFM and CDW phases, we have found an enhancement of superconducting pairing correlations, favoring (nonlocal) s-wave pairs. Our study sheds light over past inconsistencies in the literature, in particular the emergence of CDW in the pure Holstein model case.
Abstract The electron–electron and electron–phonon interactions play an important role in correlated materials, being key features for spin, charge and pair correlations. Thus, here we investigate their effects in strongly correlated systems by performing unbiased quantum Monte Carlo simulations in the square lattice Hubbard-Holstein model at half-filling. We study the competition and interplay between antiferromagnetism (AFM) and charge-density wave (CDW), establishing its very rich phase diagram. In the region between AFM and CDW phases, we have found an enhancement of superconducting pairing correlations, favouring (nonlocal) s-wave pairs. Our study sheds light over past inconsistencies in the literature, in particular the emergence of CDW in the pure Holstein model case.