Stability, phase transitions, and numerical breakdown of fractional Chern insulators in higher Chern bands of the Hofstadter model

TL;DR

This paper investigates the stability and phase transitions of fractional Chern insulators with higher Chern numbers in the Hofstadter model, confirming their existence and analyzing their properties using large-scale simulations.

Contribution

It provides the first large-scale numerical confirmation of fractional states in higher Chern bands and explores their phase transitions and stability.

Findings

Confirmed fractional states in C=1 to 5 bands at predicted fillings

Analyzed metal-insulator phase transitions in these states

Discussed the stability and potential applications of higher Chern number fractional insulators

Abstract

The Hofstadter model is a popular choice for theorists investigating the fractional quantum Hall effect on lattices, due to its simplicity, infinite selection of topological flat bands, and increasing applicability to real materials. In particular, fractional Chern insulators in bands with Chern number $|C|>1$ can demonstrate richer physical properties than continuum Landau level states and have recently been detected in experiments. Motivated by this, we examine the stability of fractional Chern insulators with higher Chern number in the Hofstadter model, using large-scale infinite density matrix renormalization group simulations on a thin cylinder. We confirm the existence of fractional states in bands with Chern numbers $C=1,2,3,4,5$ at the filling fractions predicted by the generalized Jain series [Phys. Rev. Lett. 115, 126401 (2015)]. Moreover, we discuss their metal-to-insulator phase transitions, as well as the subtleties in distinguishing between physical and numerical stability. Finally, we comment on the relative suitability of fractional Chern insulators in higher Chern number bands for proposed modern applications.