function of effective coupling and phonon frequency for $V_c=0$. The bipolaron to polaron mass ratio is about 2 in the weak coupling regime ($\lambda\ll1$) as it should be for a large bipolaron [@ver]. In the strong-coupling, large phonon frequency limit the mass ratio approaches 4, in agreement with strong-coupling arguments given above. In a wide region of parameter space, we find a bipolaron/polaron mass ratio of between 2 and 4 and a bipolaron radius similar to the lattice spacing, see Figs. 4 and 5. Thus the bipolaron is small and light at the same time. Taking into account additional intersite Coulomb repulsion $V_c$ does not change this conclusion. The bipolaron is stable for $V_c<4T(a)$. As $V_c$ increases the bipolaron mass decreases but the radius remains small, at about 2 lattice spacings. Importantly, the absolute value of the small bipolaron mass is only about 4 times of the bare electron mass $m_0$, for $\lambda=\omega/T(a)=1$ (see Fig. 4).

Simulations of the bipolaron on an infinite triangular lattice including exchanges and large on-site Hubbard repulsion $U = 20T(a)$ also lead to the bipolaron mass of about $6m_{0xy}$ and the bipolaron radius $R_{bp}\thickapprox 2a$ for a moderate coupling $\lambda= 0.5$ and a large phonon 