Speaker
Description
We study the two-dimensional Hubbard model coupled to Su–Schrieffer–Heeger phonons on the square lattice using a recently developed generalization of the single-boson exchange formalism for extended interactions. The functional renormalization group description retains the full frequency dependence of the two-particle vertex and the electronic self-energy and allows for an unbiased analysis of magnetic, charge, and superconducting fluctuations. We perform extensive parameter scans in terms of the Hubbard interaction, the electron–phonon coupling strength, and the phonon frequency, ranging from the adiabatic to the antiadiabatic regime. In the absence of the Hubbard interaction, we find that the threefold degeneracy of antiferromagnetic order, charge-density-wave order, and \textit{s}-wave superconductivity at half filling holds for all phonon frequencies. In the adiabatic limit, however, the leading instability is a valence bond solid state. For finite values of the Hubbard interaction, the $\mathbb{Z}_{2,\text{Shiba}}$ symmetry is lifted, leading to a competition between antiferromagnetism and valence bond order. Finally, at finite doping, the interplay between the Hubbard interaction and the Su–Schrieffer–Heeger phonons leads to an even richer picture characterized by intertwined ordering tendencies.