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

TL;DR

This paper investigates the magnetic phase diagram of a quarter-filled one-dimensional Wigner lattice, revealing ferromagnetic regions due to kinetic exchange and showing how magnetism influences charge order even at large U values.

Contribution

It provides new insights into the magnetic phases of Wigner lattices, highlighting the role of kinetic exchange and the impact of magnetism on charge structure beyond previous models.

Findings

Ferromagnetic ground states at negative t_2 due to kinetic exchange

Charge structure factor strongly depends on magnetism even at infinite U

Effective low-energy Hamiltonian explains the results

Abstract

The magnetic phase diagram of the quarter-filled generalized Wigner lattice with nearest- and next-nearest-neighbor hopping 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 proportional to U. Remarkably, we find a strong dependence of the charge structure factor on magnetism even in the limit U to infinity, 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.