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.