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

TL;DR

This study uses quantum Monte Carlo simulations to explore the complex phase diagram of the two-dimensional Hubbard-Holstein model, revealing how electron interactions influence magnetic, charge, and superconducting phases.

Contribution

It provides the first unbiased analysis of the competition between AFM, CDW, and superconductivity in this model, clarifying previous inconsistencies and highlighting the enhancement of s-wave pairing.

Findings

Enhanced s-wave pairing correlations between AFM and CDW phases.

Identification of a rich phase diagram with competing orders.

Clarification of the emergence of charge-density waves in the pure Holstein model.

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, 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.