Charge-order transition in the extended Hubbard model on a two-leg ladder

We investigate the charge-order transition at zero temperature in a two-leg Hubbard ladder with additional nearest-neighbor Coulomb repulsion $V$ using the density matrix renormalization group technique. We consider electron densities between quarter and half filling. For quarter filling and $U=8t,$ we find evidence for a continuous phase transition between a homogeneous state at small $V$ and a broken-symmetry state with “checkerboard” [wave vector $\mathbf{Q}=(\pi ,\pi )$] charge order at large $V.\mathrm{}$ This transition to a checkerboard charge-ordered state remains present at all larger fillings, but becomes discontinuous at sufficiently large filling. We discuss the influence of $U/t$ on the transition and estimate the position of the tricritical points.