Magnetism of one-dimensional Wigner lattices and its impact on charge order

The magnetic phase diagram of the quarter-filled generalized Wigner lattice with nearest-neighbor and next-nearest-neighbor hoppings, t1 and t2, is explored. We find a region at negative t2 with fully saturated ferromagnetic ground states that we attribute to kinetic exchange. Such interaction disfavors antiferromag- netism at t2 0 and stems from virtual excitations across the charge gap of the Wigner lattice, which is much smaller than the Mott-Hubbard gap U. Remarkably, we find a strong dependence of the charge structure factor on magnetism even in the limit U, in contrast to the expectation that charge ordering in the Wigner lattice regime should be well described by spinless fermions. Our results, obtained using the density-matrix renormalization group and exact diagonalization, can be transparently explained by means of an effective low-energy Hamiltonian.