Interband excitations in the 1D limit of two-band fractional Chern insulators

Highlights: • A fractional Chern insulator in 1D limit can be stable for infinite interaction. • Its stability can be linked to dimerization. • Excitations in the fully dimerized system can be constructed analytically. • Deviations from this case results in a decrease of the energy gap. • The results are valid for a class of models mappable to Su–Schriefer–Heeger model. - Abstract: We investigate the stability of the one-dimensional limit of $\nu =1/3$ Laughlin-like fractional Chern insulator with respect to the interband interaction. We propose a construction for the excitations in the infinite-interaction case and show that the energy gap remains finite in the thermodynamic limit. Next, by means of exact diagonalization and Density Matrix Renormalization Group approaches, we consider deviations from ideal dimerization and show that they reduce the stability of the FCI-like states. Finally, to show that our approach is not restricted to one model, we identify the dimer structure behind the thin-torus limit of other system – the checkerboard lattice.