Superfluid transition of bond bipolarons with long-range Coulomb repulsion in two dimensions

Using numerically exact diagrammatic Monte Carlo simulations in the two-electron (single-bipolaron) sector, we explore the impact of long-range Coulomb repulsion on the dilute-limit Berezinskii--Kosterlitz--Thouless (BKT) transition temperature $T_c$ of bipolarons on a two-dimensional square lattice. We study the bond Su--Schrieffer--Heeger model, in which bond phonons modulate the electron hopping. In the absence of long-range repulsion, this model was shown to support small, light bipolarons with a comparatively high transition temperature \cite{PhysRevX.13.011010}. Here we find that long-range Coulomb repulsion suppresses the optimal $T_c$ but leaves it appreciable over a broad parameter window, including the adiabatic regime $\omega/t=0.5$ at a representative Coulomb strength $V=U/10$ (with $U$ the on-site repulsion). Our results provide controlled single-bipolaron inputs for dilute-limit $T_c$ estimates in the presence of long-range repulsion.