Interplay between superconductivity and charge order near an antiferromagnetic quantum critical point: insights from Quantum Monte Carlo study

In hole-doped cuprates, besides antiferromagnetism (AFM), charge order (CO) is also observed near the superconducting (SC) dome. Under certain approximations, the spin-fermion model, in which electrons interact by exchanging AFM fluctuations, was shown to have an emergent low-energy symmetry that makes CO and SC degenerate near an AFM quantum critical point. However, the robustness of this symmetry and the CO wave-vector remains widely debated. Here, we perform sign-problem-free Quantum Monte Carlo simulations of the spin-fermion model to address these issues. We find that, when particle-hole symmetry is present, AFM fluctuations equally promote d-wave SC and d-wave CO with a diagonal wave-vector. However, small deviations from particle-hole symmetry completely lift this degeneracy, resulting in a strong suppression of CO. Inside the AFM state, the CO wave-vector shifts from diagonal to axial, presumably due to the gapping of the antinodal region of the Fermi surface. Our work shows that while SC is universally promoted near an AFM quantum critical point, CO requires additional fine-tuning of the low-energy electronic dispersion.