Two-dimensional Ising transition in one-dimensional interacting electrons

Two electron systems in one dimension, the quarter-filled extended Hubbard model with the alternating transfer integral and the half-filled ionic Hubbard model, are investigated. In both cases, their charge parts are expected to show the Ising criticality. We numerically determine the phase diagrams, and perform the finite-size scaling analysis of an excitation gap to show the evidence. Furthermore, we give the relationship between the twist operator and the Ising order parameter in a certain limit.