Adiabatic Path from Fractional Chern Insulators to the Tao-Thouless State

TL;DR

This paper investigates the existence of a lattice analogue of the Laughlin state in fractional Chern insulators, proposing an adiabatic path to identify the Chern-Laughlin state at 1/3 filling using a hybrid adiabatic transformation.

Contribution

It introduces a novel adiabatic path approach as an order parameter to characterize the Chern-Laughlin state in fractional Chern insulators.

Findings

Chern flat bands with nearest-neighbor interaction can host the Chern-Laughlin state at 1/3 filling.

The adiabatic path method can be extended to other fillings of the Jain sequence.

The approach provides a way to distinguish the Chern-Laughlin state from competing phases.

Abstract

In view of the evolution from the integer to fractional quantum Hall effect, the next frontier in the research of topological insulators is to investigate what happens in fractionally filled topological flat bands. A particularly pressing question is if there exists the lattice analogue of the Laughlin state in the 1/3-filled Chern flat band, dubbed as the Chern-Laughlin state. The answer depends crucially on the form of the electron-electron interaction, which can generate various competing ground states such as the Laughlin, stripe/nematic, parafermion, and parton states. Unfortunately, it is difficult to precisely characterize the exact ground state as any of these candidate ground states due to the lack of appropriate order parameters. Here, we propose that the existence of an adiabatic path from fractional Chern insulators to the Tao-Thouless state, i.e., the root partition state of the Laughlin state in the thin torus limit, can serve as an effective order parameter for the Chern-Laughlin state. Specifically, by devising the piecewise hybrid adiabatic path of first transforming the electron-electron interaction and then taking the thin torus limit, it is shown that Chern flat bands with the nearest-neighbor interaction can indeed host the Chern-Laughlin state at 1/3 filling. This method can be extended to possible FCIs at other general fillings of the Jain sequence.