SU(N) fractional quantum Hall effects in topological flat bands

TL;DR

This paper demonstrates the emergence of SU(N) fractional quantum Hall states in topological flat bands with interacting particles, characterized by fractional Hall responses and topological invariants, using density matrix renormalization group simulations.

Contribution

It introduces a new class of SU(N) fractional quantum Hall states in topological flat bands with specific fractional fillings, and provides topological characterization via the K matrix.

Findings

SU(N) fractional quantum Hall states appear at specific fractional fillings.

These states exhibit fractional Hall responses and charge pumping.

The topological nature is characterized by the K matrix.

Abstract

We study $N$-component interacting particles (hardcore bosons and fermions) loaded in topological lattice models with SU$(N)$-invariant interactions based on density matrix renormalization group method. By tuning the interplay of interspecies and intraspecies interactions, we demonstrate that a class of SU$(N)$ fractional quantum Hall states can emerge at fractional filling factors $\nu=N/(N+1)$ for bosons ($\nu=N/(2N+1)$ for fermions) in the lowest Chern band, characterized by the nontrivial fractional Hall responses and the fractional charge pumping. Moreover, we establish a topological characterization based on the $\mathbf{K}$ matrix, and discuss the close relationship to the fractional quantum Hall physics in topological flat bands with Chern number $N$.