Phase diagram of the two-dimensional Hubbard-Holstein model: enhancement of $s$-wave pairing between charge and magnetic orders

Abstract

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, 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.

Charge Density Wave and Superconductivity in the Disordered Holstein Model

“…Early work on the doping-driven CDW-SC transition in the Holstein model [61,62] has been extended to transitions at commensurate filling caused by the introduction of band dispersion [63], and a comparison with Migdal-Eliashberg theory [64]. Additional QMC literature has considered the Hubbard-Holstein model [65][66][67][68][69].…”

Antiferromagnetism induced by electron-phonon-coupling

“…Since unconventional SC is often closely related to antiferromagnetism [18][19][20][21][22][23], it is natural to ask whether EPC can play any essential role in driving AF ordering. Although various previous works have studied the competition between AF order dominantly induced by the Hubbard interactions and other types of orders such as CDW induced by EPC [55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70], whether AF ordering can be induced dominantly by EPC remains elusive.…”