Attractive Su-Schrieffer-Heeger-Hubbard Model on a Square Lattice Away from Half-Filling

TL;DR

This study investigates the attractive SSH-Hubbard model on a square lattice away from half-filling, revealing how charge order, bond order, and s-wave pairing evolve and compete under doping using quantum Monte Carlo simulations.

Contribution

It provides the first detailed numerical analysis of the attractive SSH-Hubbard model away from half-filling, highlighting the interplay and competition among charge order, bond order, and s-wave pairing.

Findings

Charge order appears at weak electron-phonon coupling.

Bond order dominates at large coupling.

Doping favors s-wave pairing over charge and bond orders.

Abstract

The Su-Schrieffer-Heeger (SSH) model, with bond phonons modulating electron tunneling, is a paradigmatic electron-phonon model that hosts an antiferromagnetic order to bond order transition at half-filling. In the presence of repulsive Hubbard interaction, the antiferromagnetic phase is enhanced, but the phase transition remains first-order. Here we explore the physics of the SSH model with attractive Hubbard interaction, which hosts an interesting interplay among charge order, s-wave pairing, and bond order. Using the numerically exact determinant quantum Monte Carlo method, we show that both charge order, present at weak electron-phonon coupling, and bond order, at large coupling, give way to s-wave pairing when the system is doped. Furthermore, we demonstrate that the SSH electron-phonon interaction competes with the attractive Hubbard interaction and reduces the s-wave pairing correlation.