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

Abstract

The magnetic phase diagram of the quarter-filled generalized Wigner lattice with nearest-neighbor and next-nearest-neighbor hoppings, ${t}_{1}$ and ${t}_{2}$, is explored. We find a region at negative ${t}_{2}$ with fully saturated ferromagnetic ground states that we attribute to kinetic exchange. Such interaction disfavors antiferromagnetism at ${t}_{2}<0$ and stems from virtual excitations across the charge gap of the Wigner lattice, which is much smaller than the Mott-Hubbard gap $\ensuremath{\propto}U$. Remarkably, we find a strong dependence of the charge structure factor on magnetism even in the limit $U\ensuremath{\rightarrow}\ensuremath{\infty}$, 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.