Halperin $(m^{\prime },m,n)$ fractional quantum Hall effect in topological flat bands

Abstract

The Halperin $(m^{\prime },m,n)$ fractional quantum Hall effects of two-component quantum particles are studied in topological checkerboard lattice models. Here for $m\ne m^{\prime }$, we demonstrate the emergence of fractional quantum hall effects with the associated $\mathbf{K}=\left(\begin{array}{cc}m+2& 1\\ 1& m\end{array}\right)$ matrix (even $m=2$ for boson and odd $m=3$ for fermion) in the presence of both strong intercomponent and intracomponent repulsions. Through exact diagonalization and density-matrix renormalization group calculations, we elucidate their topological fractionalizations, including (i) the $\det |\mathbf{K}|=(m^2+2m-1)$-fold ground-state degeneracies and (ii) fractionally quantized topological Chern number matrix $\mathbf{C}={\mathbf{K}}^{-1}$. Our flat band model provides a paradigmatic example of a microscopic Hamiltonian featuring fractional quantum Hall effect with partial spin-polarization.

arXiv comment8 pages, 8 figures; revised version. arXiv admin note: text overlap with arXiv:2012.08203, arXiv:2204.01514

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