Orbital antiferroelectricity and higher dimensional magnetoelectric order in the spin-$1/2$ XX chain extended with three-spin interactions

We study the spin-1/2 XX model extended with three-spin interactions of the XZX+YZY and XZY-YZX types. We solve the model exactly and obtain the ground state phase diagram as a function of the two three-spin coupling strengths. We show that even in absence of external electric and magnetic fields there is a phase which exhibits spontaneous magnetoelectric order when both XZX+YZY and XZY-YZX interactions are present. Specifically, in this regime, we show that there exists not only a non-zero magnetization and a scalar chirality but also a vector chiral order. Further, we show the existence of a plaquette vector chirality, or circulating chiral spin current loops, in the plaquettes n, n+1, n+2 with the sense of the current being opposite in adjacent plaquettes. Analogous to charge current loops giving rise to orbital magnetic dipole moments, the circulating spin current loops give rise to orbital electric dipole moments - a novel orbital antiferroelectricity. We characterize this phase by a higher-dimensional scalar and vector toroidal order. Such a novel phase with higher dimensional order arises because of the non-trivial topological connectivity resulting from the presence of both the three-spin interactions. We also study the combined effect of both types of three-spin interactions on the entanglement entropy.