Fig. 9: Charge gap Δc.

A charge gap opens up at the transition between a Luttinger Liquid and a \({{\mathbb{Z}}}_{3}\) Mott insulator around \(J=\sqrt{2}\,t\), for \(\nu =\frac{2}{3}\). The Mott phase, which at h/t, h/J ≪ 1 spans the range \(\frac{{J}^{\star }}{t} < \frac{J}{t} < \sqrt{2}\) extends in a lobe structure to finite values of the electric field strength h/t. The system size is set to L = 120.